atlas Library
Function Index
Every name defined in the 175 script files read when
loading all.at: functions, operators, values, types and type fields (3468 names). Each link goes to
the definition in its file; ×n counts the overloads in that file.
Symbols (operators)
!basic ×4!=basic · combinatorics ×3 · synthetic · hash · tits · cyclotomic ×2 · polynomial ×4 · cyclotomicMat#basic ×5 · W_reps · misc ×3 · cells##basic ×4 · ratmat ×3%basic ×2 · extParamPol · misc · polynomial ×3*basic ×13 · extParamPol ×3 · complex · modules ×2 · hodge_tensor · tits_centralizer · stable ×3 · synthetic · Weylgroup ×2 · group_operations ×3 · ratmat ×11 · tits · twisted_root_datum · cyclotomic ×2 · polynomial ×12 · hodgeParamLaurentPol ×10 · hodgeParamPol ×9 · laurentPolynomial ×4 · cyclotomic_Lie_algebra ×4 · cyclotomicMat ×7 · bracket · hodge_functions ×2 · sparse ×2 · lazy_lists ×2+basic ×8 · extParamPol ×3 · modules ×3 · ratmat ×6 · cyclotomic · polynomial ×10 · hodgeParamLaurentPol ×2 · hodgeParamPol ×2 · laurentPolynomial ×4 · cyclotomic_Lie_algebra · cyclotomicMat ×3 · bracket · hodge_functions · lazy_lists ×3-basic ×9 · extParamPol · modules ×5 · ratmat ×7 · cyclotomic ×2 · polynomial ×13 · hodgeParamLaurentPol ×2 · hodgeParamPol ×2 · laurentPolynomial ×2 · cyclotomicMat ×5 · hodge_functions · lazy_lists ×4/basic ×2 · ratmat ×4 · cyclotomic ×2 · polynomial ×2 · lazy_lists ×3<basic ×3 · nilpotent_orbits<=basic ×3 · combinatorics ×2 · nilpotent_orbits=basic ×3 · combinatorics ×4 · modules ×3 · parabolics · synthetic · hash · tits · K_highest_weights · nilpotent_orbits ×2 · cyclotomic ×3 · polynomial ×5 · W_reps_type_BC · hodgeParamLaurentPol ×2 · hodgeParamPol ×2 · laurentPolynomial · extended · disconnected · cyclotomic_Lie_algebra ×2 · cyclotomicMat ×2 · bracket ×2==basic ×2===basic>basic>=basic\basic ×3 · polynomial ×3 · lazy_lists\%basic ×3 · polynomial^basic ×7 · ratmat ×3 · tits · cyclotomic · polynomial ×2 · sparse · lazy_lists~basic ×3
A
Afield ofNilpotentDatum, exceptionalalaurentPolynomialA1lietypesA2lietypesA3lietypesA4lietypesA5lietypesA6lietypesA7lietypesA8lietypesA_barlusztig_cells ×2a_column_withbasicA_Levi_factorW_reps_type_BCa_primegeck_generica_row_withbasica_solutionGaussian_elim · cyclotomic_Gaussian_elim ×3 · cyclotomic_Lie_algebraAbarfield ofNilpotentDatum, exceptionalabsbasic ×2absolute_value_squaredcyclotomicAC_Levi_factorW_reps_type_BCACLfW_reps_type_BCacquirefield ofHash, hashact_upLevi_subgroupsaction_fundamental_groupaffineaction_on_root_vectorstits_centralizer ×4actorfield ofStdLeviImage, Levi_subgroups · field ofStdLeviEltImage, W_classesadfield ofAffineWeylElt, affine · cyclotomic_Lie_algebra · bracketAdamsW_classesadapted_direct_sumlatticeadapted_direct_sum_pluslatticeaddhodge_K_type_formulaadd_onesommersadd_to_matrix_entrymatrixadd_weighttensor_product ×6add_weightstensor_product ×5add_wt_to_paramtensor_productadjointbasic ×2 · group_operations ×2adjoint_2rhobasicadjoint_imagesubgroupsadjoint_infogroup_operationsadjoint_transformgroup_operationsaffine_co_make_dominantaffine ×2affine_coordinatesaffine ×7affine_coreflectaffine ×2affine_coroot_sumaffineaffine_corootsfield ofAffineDatum, affineaffine_datumtwisted_root_datum ×2 · affine ×2affine_datum_longtwisted_root_datumaffine_datum_shorttwisted_root_datumaffine_labelsaffineaffine_make_dominantaffineaffine_non_dominant_indexaffine ×2affine_reflectaffine ×2affine_root_of_factortwisted_root_datumaffine_root_sumaffineaffine_rootsfield ofAffineDatum, affineaffine_spacefield ofCF_lin_solution, cyclotomic_Gaussian_elimaffine_subspacetype, Gaussian_elimaffine_verboseaffineAffineDatumtype, affineAffineSubspacetype, basicAffineWeylElttype, affineALfW_reps_type_BCallbasic ×5all_0_1_vecsbasicall_0_1_vecs_with_sumbasicall_discrete_seriesK_highest_weightsall_dominant_height_uptoK_norm ×2all_dominant_norm_uptoK_highest_weightsall_equal_dlambda_K_parametersK_highest_weightsall_G_spherical_same_differentialK_highest_weights ×2all_Hnilpotent_orbitsall_H_ndnilpotent_orbitsall_H_with_Lnilpotent_orbitsall_induced_unipotents_longweak_packetsall_inner_classesgenerate_groupsall_K_normsK · K_norm ×2all_lambda_differential_0K_highest_weightsall_Levi_Springer_tablesgeck_genericall_levi_tablesgeck_genericall_levi_tables_plusgeck_genericall_minimal_principal_seriesK_highest_weightsall_parabolicsparabolicsall_parabolics_with_theta_stable_Leviparabolicsall_parametersK_highest_weightsall_parameters_gammaK_highest_weightsall_parameters_x_gammaG2_unitary_dual · K_highest_weightsall_posrootsbasicall_productssubgroupsall_real_induced_one_dimensionalinductionall_real_nilpotent_orbit_KGBsnilpotent_orbitsall_real_parabolicsparabolicsall_rel_split_theta_stable_parabolicsparabolicsall_reps_BCW_reps_type_BC ×2all_root_indextits_centralizer ×2 · misc ×2all_rootsbasicall_simplegenerate_groupsall_simple_adjoint_rankgenerate_groupsall_simple_given_isogeny_and_rankgenerate_groupsall_simple_root_systems_given_rankgenerate_groupsall_simple_simply_connected_rankgenerate_groupsall_simplesbasicall_solutionscyclotomic_Gaussian_elimall_sumsnci_nilrad_rootsall_wf_Aq_with_ic_ofaqlall_wordsbasic ×3alt_namefield ofNilpotentDatum, exceptionalamong_poscorootsbasicamong_posrootsbasicanalysehermitiananalyse_hermitian_form_irreduciblehermitiananisotropic_partfinite_dimensional_signatureanisotropic_part_stringfinite_dimensional_signatureanisotropic_part_tracefinite_dimensional_signatureanisotropic_part_trace_stringfinite_dimensional_signatureanybasic ×5 · cyclotomic_Lie_algebra · nilpotent_inductionappendbasicapplyGaussian_elim ×2 · cyclotomic_Gaussian_elim ×2Aqinduction ×4Aq_cellsnilpotent_orbits ×2Aq_longadams_johnson ×4Aq_packetinduction ×2Aq_reducibleinductionAq_reducible_longadams_johnson ×3Aq_repsnilpotent_orbitsAq_rhoadams_johnson ×2Aq_rho_stableadams_johnson ×2Aq_rho_stable_testadams_johnson ×2Aq_stableadams_johnson ×2Aq_stable_longadams_johnson ×2Aq_stable_testadams_johnson ×2Aq_zerosinductionaql_verboseaqlarithmetic_progressionlazy_listsarray_printsmodulesarthur_parametersarthur_parameters ×2arthur_parameters_by_orbitarthur_parametersarthur_parameters_by_yarthur_parametersas_bipartitioncombinatoricsas_columnbasicas_listbasicas_polbasic ×4 · modulesas_predictedtest_unitarityas_rowbasicas_signed_cyclescombinatoricsascentsparabolicsassertbasic ×6associated_variety_annassociated_variety_annihilator ×5associated_variety_ann_indassociated_variety_annihilator ×6associated_variety_ann_resassociated_variety_annihilator ×6associated_variety_ann_res_complexassociated_variety_annihilatorassociated_variety_ann_res_testassociated_variety_annihilatorassociated_variety_intassociated_variety_annihilator ×4at_q_inverselaurentPolynomialat_spolynomialat_v_squaredpolynomialautomorphismsfield ofDisconnectedGroup, disconnectedavK_Nilpotent ×3av_annK_Nilpotent ×2av_ann_elemK_Nilpotent ×2av_ann_elem_longK_Nilpotent ×2av_elemK_Nilpotent ×2av_elem_longK_Nilpotent ×2av_from_av_annK_Nilpotent ×2av_from_av_ann_elemK_Nilpotent ×2av_from_av_ann_elem_longK_Nilpotent ×2av_maximal_idealassociated_variety_annihilator ×4av_maximal_ideal_0associated_variety_annihilator ×3av_verboseassociated_variety_annihilator
B
blaurentPolynomialB2lietypesB3lietypesB4lietypesB5lietypesB6lietypesB7lietypesB8lietypesB_adjustspringer_table_BCB_to_C_dualspringer_table_BCbackward_differencesbasicBala_Carter_Levinilpotent_orbitsBala_Carter_Levi_plusnilpotent_orbitsBala_Carter_simplesnilpotent_orbitsbarcyclotomic · cyclotomicMatbase_pointfield ofAffineSubspace, basic · field ofaffine_subspace, Gaussian_elimbasic_nodesposetbasisbracketbasis_dual_latticetits_centralizer ×2basis_lambda_differential_0K_highest_weightsbasis_max_split_torusrestricted_rootsBC_classesclass_tablesBC_irrepsclassical_character_tablesBezoutnumber_theory · polynomialbig_blockbasicbig_KL_P_polynomialsbigMatricesbig_KL_P_polynomials_at_minus_onebigMatricesbig_KL_P_signed_polynomialsbigMatricesbig_KL_P_signed_polynomials_at_minus_onebigMatricesbig_KL_Q_polynomialsbigMatricesbinarybasicbinary_lookupbasic ×3binary_lookup_bybasicbinary_search_firstbasicbinary_search_getbasicbinary_search_inbasic ×2binomcombinatorics ×2BiPartitiontype, combinatoricsbipartition_as_irrep_labelclassical_character_tablesbirational_inductionsommers ×2bitwise_intersectionbasicbitwise_unionbasicblock_action_matrix_irrfourblock_action_matrix_stdfourblock_and_cellscellsblock_decomposeL_packetblock_matrixbasic ×2block_ofbasicblock_status_textbasicblocksbasic ×2 · cells · weak_packets ×2blocks_and_cellscells ×2blockunilpotent_orbitsbounded_coset_repsparabolicsbounded_generateW_orbit ×2bounded_generate_action_from_domW_orbitbounded_generate_from_domW_orbitbounded_listsall_finite_orderboxmisc ×2bracketcyclotomic_Lie_algebra · bracketbracket_off_diagonal_termscyclotomic_Lie_algebra · bracketbracket_root_termcyclotomic_Lie_algebra · bracketbracket_torus_termcyclotomic_Lie_algebra · bracketbranchbasic ×2 · modulesbranch_c_form_irreduciblehermitianbranch_function_stdhodge_tensor · hodge_functionsbranch_function_std_as_hodge_functionhodge_functionsbranch_irrK_types ×2branch_stdK_types ×3bruhatbruhat ×3bruhat_geqbruhat ×3bruhat_leqbruhat ×3Bruhat_orderbasicbruhat_Wbruhatbruhat_W_geqbruhatbruhat_W_leqbruhatby_fieldgroups
C
CgroupsclaurentPolynomialC2lietypesC3lietypesC4lietypesC5lietypesC6lietypesC7lietypesC8lietypesC_adjustspringer_table_BCc_adjustbasic · tabulatec_form_branch_irrc_form_branchc_form_branch_stdc_form_branch ×2c_form_irreduciblehermitian ×2c_form_irreducible_bigextParamPol ×2c_form_irreducible_big_as_sum_of_standardsextParamPolc_form_irreducible_big_longextParamPolc_form_irreducible_longhermitianc_form_stdhermitianc_form_std_bigextParamPolC_Levi_signatureW_reps_type_BCC_to_B_dualspringer_table_BCcalculate_big_P_signed_polynomialsbigMatricescalculate_big_P_signed_polynomials_at_minus_onebigMatricescanbasiccan_locatesubgroupscanonical_gextended_misc ×4capacityfield ofHash, hashCartan_classbasic ×3Cartan_classesbasicCartan_matrixbasicCartan_matrix_typelietypescartansG2_unitary_dualCartesian_powerfield ofWeylClassTable, W_classes · character_tables ×2Cayleybasic · extended_miscCayley_setextended_misc ×3Cayley_sumcoherentcc_BCfinite_unipotentscc_Dfinite_unipotentsceilbasiccell_actionW_reps ×3 · character_table_reps ×2cell_and_character_dataweak_packets_precomputed_cell_traces ×2cell_as_wcomplexcell_characterW_reps · cells · character_table_repscell_character_inefficientcells ×2cell_charactersW_repscell_characters_inefficientcellscell_closurecell_graphcell_members_given_descentcellscell_reductioncell_graphcell_representationW_repscell_representationsW_repscellsweak_packets ×3cells_given_AVcellscells_tableW_repscells_table_augmentedW_repscells_verbosecellscentercentercenter_torsion_quotientcentercentral_cocharacterVogan-dualcentral_invariantgalois ×2central_invariant_indexgalois ×2central_torus_rankbasic ×2centralizergood_W_representatives · nilpotent_centralizer · K_highest_weights · subgroups ×3 · conjugate · cyclotomic_Lie_algebra · bracket · weyl_character_formulacentralizer_coweightsubgroupscentralizer_of_Kacall_finite_ordercentralizer_ordercombinatorics · W_classes · character_tablescentralizer_pseudo_Levisubgroupscentralizer_rootsnilpotent_centralizercentralizer_roots_and_corootsnilpotent_centralizer ×2centralizer_weightsubgroupscertificatecertificateCFcyclotomicCF_lin_solutiontype, cyclotomic_Gaussian_elimCFbasiscyclotomic_Lie_algebraCFLieAlgebraElementtype, cyclotomic_Lie_algebrachainsommerschamberbasic ×6chamber_max_systemLevi_subgroupschange_basisK_Nilpotent · coordinates ×3change_nuextParamPolcharhodge_K_type_formulachar_indexbasicchar_polybasic · Weylgroupcharactercombinatorics · modules · W_reps · character_tables · character_table_repscharacter_coherentcoherent_characters ×4character_coherent_Bcoherent_characters ×2character_coherent_dualcoherent_characters ×2character_coherent_dual_rcoherent_characterscharacter_coherent_gammacoherent_characters ×2character_coherent_Icoherent_characterscharacter_coherent_rcoherent_characters ×2character_coherent_r_Xcoherent_characterscharacter_coherent_Tcoherent_characterscharacter_coherent_T_dualcoherent_characterscharacter_coherent_T_dual_rcoherent_characterscharacter_coherent_T_rcoherent_characterscharacter_coherent_Xcoherent_characterscharacter_coherent_Ycoherent_characters ×2character_formulaextParamPol · modules ×2 · kl ×2character_formula_one_dimensionalK_type_formulacharacter_formula_trivialK_type_formulacharacter_indexcharacter_tablescharacter_tablecharacter_tables ×3 · springer_tables · character_tables_reductivecharacter_table_Aclassical_character_tablescharacter_table_Bclassical_character_tables ×2character_table_Cclassical_character_tables ×2character_table_Dclassical_character_tables ×2character_table_E6character_table_E6 ×3character_table_E7character_table_E7 ×3character_table_E8character_table_E8 ×3character_table_Fcharacter_table_F ×3character_table_F4_datacharacter_table_Fcharacter_table_Gcharacter_table_G ×3character_table_generic_degreesgeck_genericcharacter_table_Sclassical_character_tablescharacter_table_simplecharacter_tables_reductivecharacter_valueW_classescharacterscharacter_tables · springer_tables · field ofDisconnectedGroup, disconnectedcharacters_order_2K_highest_weightsCharacterTabletype, character_tablescharpolyfield ofEllipticDatum, exceptionalcheck_dual_lambdaVogan-dualcheck_F4_degreescharacter_table_Fcheck_hermitianhermitiancheck_nilradical_dimensionsnilpotent_centralizer ×2check_orthogonalitycharacter_tableschoices_frombasicchoose_Cayleynilpotent_orbitschoose_gparameters ×3choose_gammanilpotent_orbits ×2choose_irred_indsK_highest_weightschoose_irred_inds_plusK_types_plusclass_labelfield ofCharacterTable, character_tablesclass_offield ofWeylClassTable, W_classes · character_tablesclass_ordercharacter_tablesclass_powerfield ofWeylClassTable, W_classes · character_tablesclass_representativeW_classes · character_tablesclass_representativesfield ofWeylClassTable, W_classes · character_tablesclass_signature_E6class_tablesclass_signature_E7class_tablesclass_signature_E8class_tablesclass_signature_F4class_tablesclass_sizecombinatorics · W_classes · character_tablesclass_sizesfield ofWeylClassTable, W_classes · character_tablesclass_tablefield ofCharacterTable, character_tablesclass_table_Aclass_tablesclass_table_Bclass_tables ×2class_table_Cclass_tables ×2class_table_Dclass_tables ×2class_table_Eclass_tablesclass_table_E6class_tables ×3class_table_E7class_tables ×3class_table_E8class_tables ×3class_table_Fclass_tables ×2class_table_Gclass_tables ×2class_table_Sclass_tablesclass_table_simpleclass_tablesclass_wordclass_tablesclass_word_BCclass_tablesclass_word_Dclass_tables ×2classes_for_real_parabolicsparabolicsclasses_for_theta_parabolicsparabolicsclasses_Kondo_F4class_tablesclassic_permutationcombinatoricsclassical_partsommersclassical_part_Bsommersclassical_part_CsommersClassicalOrbitSymboltype, sommersclassify_standard_LevisLevi_subgroupsclearfield ofHash, hashclosureK_Nilpotent · poset · field ofNilpotentDatum, exceptional · exceptionalclosure_of_real_orbitK_Nilpotentclosure_realK_Nilpotentclosuresnilpotent_orbit_partitionsco_affine_labelsaffineco_invariant_formWeylgroupco_invariant_form_matrixWeylgroupco_labelsaffineco_usual_coordinatesaffinecocharacter_lattice_KK ×2codimensionbasic ×2coefficienthodgeParamLaurentPol ×2 · hodgeParamPol ×3 · hodge_functions · lazy_listscoefficientsfield ofint_poly, polynomial · field ofrat_poly, polynomialcoherent_datacoherent_characters ×2coherent_family_irrcoherentcoherent_irrcoherent_irreducible ×7 · coherent ×6coherent_irr_newcoherent_irreducible ×6coherent_stdcoherent ×7coherent_std_compact_Cartaninductioncoherent_std_imaginaryinductioncoherent_verbosecoherent_characterscoinject_from_KK ×2cokernelbasiccollapsespecial_repcollectbasiccolumnhodge_K_type_formula · stable · ratmatcolumnsratmatcolumns_withbasic ×3 · ratmat ×3combination_decodecombinatoricscombination_encodecombinatoricscombinegenerics · character_tables_reductive · class_tables · springer_tables_reductivecombine_W_listsellipticcompact_coradical_basiscentercompact_formbasiccompact_inner_classshow_nilpotent_orbitscompact_posrootsbasiccompact_radical_basiscentercompact_rankbasic ×2compact_stringbasiccompact_torusbasiccompareparameterscompare_longparameterscomplementbasic ×2 · misc · parameterscomplete_indicesbigMatricescomplexgroupscomplex_conjugatecyclotomiccomplex_KTfinite_dimensionalcomplex_Leviparabolics · nilpotent_orbitscomplex_LKTfinite_dimensionalcomplex_nilpotentnilpotent_orbitscomplex_nilpotent_from_diagramnilpotent_orbitscomplex_nilpotent_from_partitionsommers · nilpotent_orbit_partitionscomplex_orbitnilpotent_orbitscomplex_orbit_numberK_Nilpotent ×3complex_orbitsfield ofKNilpotentData, K_Nilpotentcomplex_parabolicparabolics ×2complex_posrootsbasic ×2complex_pseudo_Leviall_finite_ordercomplexificationgroupsComplexNilpotenttype, nilpotent_orbitsComplexNilpotent_dtype, disconnectedComplexNilpotentComponentDatumtype, nilpotent_orbitsComplexParabolictype, parabolicscomponent_datumnilpotent_orbitscomponent_datum_plusnilpotent_orbitscomponent_group_of_pseudo_Levisubgroupscomponent_representativesnilpotent_orbitscomponent_representatives_plusnilpotent_orbitscomposegenericscompose_permutationscombinatoricscomposition_seriesmodules ×2 · kl ×2composition_series_traceklcomposition_series_verboseklcompositional_inverselazy_listscompresshodge_deformcompressed_stringcombinatorics ×2compute_structure_constantstructure_constantscompute_Y_matrixK_Nilpotentconcatbasic · syntheticconcatenatecomplexconeK_highest_weightsconfirmaffine ×2conjugacy_class_Aclass_tablesconjugacy_class_Bclass_tablesconjugacy_class_Cclass_tablesconjugacy_class_Dclass_tablesconjugacy_class_numberW_classesconjugacy_class_ordersnilpotent_orbitsconjugacy_class_repsW_classesconjugacy_class_Sclass_tablesconjugacy_class_SOclass_tablesconjugacy_classes_from_subssubgroupsconjugacy_classes_involutionsgaloisconjugacy_classes_reflectionsgeck_generic ×2conjugacy_classes_reflections_simplegeck_genericconjugacy_testW_classesconjugacy_witnessW_classes ×2conjugacy_witness_inW_classesConjugacyTestertype, W_classesConjugacyWitnessertype, W_classesconjugatebasic ×2 · tits ×2conjugate_from_elected_LeviW_classesconjugate_from_some_standard_LeviW_classesconjugate_toW_orbit ×2conjugate_to_simplecharacter_table_repsconstantgenericsconstant_laurent_polylaurentPolynomialconstant_polypolynomial ×3constant_termlazy_listsconstruct_class_tableclass_tablescontainsbasic ×2contragredientparametersconvertW_K · nilpotent_orbits ×4convert_cform_hermitianconvert_c_form ×4convert_K_typeK ×2convert_list_W_cellsnilpotent_orbitsconvert_tobasicconvolvepolynomialcoordinatescyclotomic_Lie_algebra · bracket ×3coordsG2_unitary_dualcoradical_basisbasiccoresommerscore_lengthcombinatoricscore_numbercombinatoricscore_quotient_2combinatoricscoreflectbasic ×4 · affine ×4coreflect_or_affine_coreflectaffinecoreflect_or_coaffine_reflectaffinecoressommerscorestrict_actionlatticecorootbasiccorootsbasiccoroots_all_positivebasiccosexp-generating-seriescoset_repsparabolicscould_addhashcountbasic ×3count_orbits_and_centralizersfinite_unipotentscount_permutations_with_cyclesexp-generating-series ×2count_unipotentsfinite_unipotentscoverdirac_indexcover_cdirac_indexcoxall_finite_ordercoxeter_dataweyltosemisimplecoxeter_elementWeylgroupcoxeter_numberWeylgroupcoxeter_number_simpleWeylgroupcoxeter_torus_elementWeylgroupcrossbasic ×5 · coherent_irreducible ×9 · synthetic · extended_misc · coherent_characterscross_dividecross_W_orbitcross_divide_altK_types_pluscross_gradedcoherent_irreducible ×2cross_orbitcross_W_orbitcross_squarecoherent_irreducible ×4cross_square_testcoherent_irreducible ×2cross_sub_orbitcross_W_orbitctfield ofSpringerTable, springer_tablescumulate_backwardbasiccumulate_forwardbasiccurried_swapargsgenericscurrygenericscuspidal_datainductioncuthodge_K_type_formulacut_off_last_stringW_reps_type_BCcut_off_stringW_reps_type_BCcutoffaffinecycle_centralizer_ordercombinatorics ×2cycle_class_sizecombinatorics ×2cycle_codecombinatoricscycle_powercombinatorics ×3cycle_productcombinatoricscycle_typecombinatoricscycle_type_GLclass_tablescycle_type_ordercombinatorics ×3cycles_stringclassical_W_classes_and_reps ×2cyclic_permutationcombinatoricscyclic_twisttwisted_root_datum ×2cyclotomic_factorscyclotomiccyclotomic_fieldcyclotomiccyclotomic_field_elementcyclotomiccyclotomic_matrixcyclotomicMatCyclotomic_Pivot_infotype, cyclotomic_Gaussian_elimcyclotomic_pivot_stepcyclotomic_Gaussian_elimcyclotomic_polynomialnumber_theorycyclotomic_vectorcyclotomicMatCyclotomicFieldtype, cyclotomicCyclotomicFieldElementtype, cyclotomicCyclotomicMattype, cyclotomicMatCyclotomicVectype, cyclotomicMat
D
dfield ofgood_data, weyltosemisimpleD2lietypesD3lietypesD4lietypesD4_spherical_unitaryunitaryD5lietypesD6lietypesD7lietypesD8lietypesD_adjustspringer_table_DD_classtype, combinatoricsD_classescombinatoricsD_dualspringer_table_DD_irreduciblescombinatoricsD_irreptype, combinatoricsD_irrepsclassical_character_tablesd_Lnilpotent_orbits ×2d_lambdabasicdearrangehodgeParamLaurentPol · hodgeParamPoldebugshow_nilpotent_orbitsdecomposelattice ×2 · character_tablesdefaultsubgroups · extendeddefault_orbit_symbolsommersdefault_orbit_symbol_Bsommersdefault_orbit_symbol_Csommersdefault_weight_functiongeck_genericdeformextParamPol ×2deform_oldextParamPoldeform_to_heightbasicdeform_unreducedextParamPoldeformation_termsext_deformdeg_specfield ofCharacterTable, character_tablesdegreecyclotomic · polynomial ×3 · character_tables · laurentPolynomialdeletebasic ×3 · hodge_K_type_formuladelete_allsommers ×2delete_leading_zerosmiscdelete_nodeposetdelete_nodesposetdelete_trailing_zerosmiscdeltafield ofgood_data, weyltosemisimple · field ofTwistedRootDatum, twisted_root_datum · field ofExtParam, extended_miscdelta_orbit_repsbigMatricesDemazurefinite_dimensionaldenomfield ofAffineSubspace, basic · basic ×2derangement_numbersexp-generating-seriesderivedbasic · group_operations ×2derived_infogroup_operationsderived_is_simplebasic ×2derived_is_simply_connectedbasicdescendbruhatdescribe_isogenynilpotent_centralizer ×2detbasic · ratmat · Gaussian_elim · cyclotomic_Gaussian_elimdiagcomplexdiag_Wcomplexdiagonalratmatdiagonal_matcyclotomicMatdiagramnilpotent_orbits · field ofNilpotentDatum, exceptionaldiagram_A_to_partitionspringer_table_Adiagram_automorphism_iteratordiagram ×2diagram_B_to_partitionspringer_table_BCdiagram_C_to_partitionspringer_table_BCdiagram_componentsimple_factorsdiagram_componentssimple_factorsdiagram_D_to_partitionspringer_table_Ddiagram_normalizednilpotent_orbitsdiagram_to_name_E8springer_table_E8digit_to_intspringer_table_E8digits36basicdigraphsub_cellsdimnilpotent_orbitsdim_centralizernilpotent_centralizerdim_centralizer_nilradicalnilpotent_centralizerdim_eigenspacenilpotent_orbitsdim_K_types_std_uptoGK_dimensiondim_nilpotentnilpotent_orbitsdim_nilpotent_partitionsommers · nilpotent_orbit_partitionsdim_nilradical_parabolic_Hnilpotent_centralizerdim_repW_reps_type_BCdim_uinduction ×3dim_u_cap_kinduction ×3dim_u_cap_k_1inductiondim_u_cap_k_2inductiondim_u_cap_k_ge2inductiondim_u_cap_pinduction ×3dim_u_cap_p_1inductiondim_u_cap_p_ge2inductiondimensionbasic ×2 · field ofW_rep, W_reps · finite_dimensional ×2 · K_highest_weights ×2 · nilpotent_orbits · field ofWeylClassTable, W_classes · character_tables ×2 · W_reps_type_BC · tensor_product · exceptionaldimension_u_cap_stensor_productdimension_wedge_u_cap_stensor_productdimensionsK_highest_weights ×3dirac_index_dsdirac_index ×2dirac_index_irrdirac_index ×2dirac_index_stddirac_index ×2direct_sumfield ofWeylClassTable, W_classesDisconnectedGrouptype, disconnecteddiscrete_seriesrepresentations ×2displayextParamPol · extended_miscdisplay_one_lineextended_miscdisplay_stringK_Nilpotentdistinguished_fiberbasicdistinguished_H_diagramsnilpotent_orbitsdistinguished_H_domnilpotent_orbitsdistinguished_Hsnilpotent_orbitsdistinguished_Hs_definitionnilpotent_orbitsdistinguished_nilpotent_orbitsnilpotent_orbitsdistinguished_orbitsnilpotent_orbitsdividepolynomial · lazy_listsdivide_bybasic ×2 · polynomial · lazy_lists ×2divisorsnumber_theorydominance_leq_compositionscombinatoricsdominance_leq_partitionscombinatoricsdominantbasic ×6 · nilpotent_orbitsdonefield ofmaybe_KTP, hermitian · bigMatricesdot_productpolynomial ×2 · cyclotomicMat ×3down_neighborsparabolicsdownscale_bylazy_listsdrop_lowerbasic ×2drop_upperbasic ×2dualhodge_K_type_formula · hodge_tensor · twisted_root_datum · Vogan-dual ×4 · field ofNilpotentDatum, exceptionaldual_blockdual ×2dual_datasommersdual_diagram_E8springer_table_E8 ×2dual_diagram_table_E8springer_table_E8dual_E8springer_table_E8dual_ExtParameterdualdual_gammaVogan-dualdual_inner_classparametersdual_integralbasicdual_KGBVogan-dualdual_KLbasicdual_lambdaVogan-dualdual_mapfield ofSpringerTable, springer_tablesdual_map_Aspringer_table_Adual_map_Bspringer_table_BC ×2dual_map_Cspringer_table_BC ×2dual_map_Dspringer_table_Ddual_map_E7springer_table_E7dual_map_ifield ofSpringerTable, springer_tablesdual_nilpotent_orbit_partitionsnilpotent_orbit_partitions ×2dual_orbitsommers ×3dual_orbitsnilpotent_orbitsdual_parameterextended_miscdual_parametersstabledual_parameters_matrixstable ×3dual_parameters_standard_basisstable ×2dual_parameters_standard_basis_poly_matstabledual_real_formsbasic ×2dual_shiftVogan-dualdual_signextended ×2dual_special_piecespringer_tablesdual_symbolssommersdual_torus_factorextendedduality_permutationstabledvdirac_index
E
Eextended ×7E6lietypesE6_cgroupsE6_C4groupsE6_D5TgroupsE6_elliptic_wordsellipticE6_F4groupsE6_hgroupsE6_ic_egroupsE6_ic_sgroupsE6_lusztig_map_ellipticexceptionalNilpotentDataE6_nilpotent_dataexceptionalNilpotentDataE6_nilpotent_orbit_dual_mapspringer_table_E6e6_profilecharacter_table_E6E6_qgroupsE6_sgroupsE6_sc_q_dataE6_sc_q_unipdataE6_sc_s_dataE6_sc_s_unipdataE6_Springer_mapspringer_table_E6e6_tablecharacter_table_E6E7lietypesE7_A7groupsE7_cgroupse7_characterscharacter_table_E7E7_D6A1groupsE7_E6TgroupsE7_elliptic_wordsellipticE7_hgroupse7_half_tablecharacter_table_E7E7_icgroupsE7_ic_egroupsE7_lusztig_map_ellipticexceptionalNilpotentDataE7_nilpotent_dataexceptionalNilpotentDataE7_nilpotent_orbit_dual_mapspringer_table_E7E7_positionscharacter_table_E7e7_profilecharacter_table_E7E7_qgroupsE7_sgroupsE7_sc_h_dataE7_sc_h_unipdataE7_sc_q_dataE7_sc_q_unipdataE7_sc_s_dataE7_sc_s_unipdataE7_signaturetype, class_tablesE7_spherical_unitaryunitaryE7_Springer_mapspringer_table_E7E8lietypesE8_cgroupsE8_diagramsspringer_table_E8E8_dimensionsspringer_table_E8E8_dual_namesspringer_table_E8E8_elliptic_wordselliptice8_gap_centralizer_sizese8_gape8_gap_class_nre8_gape8_gap_classese8_gape8_gap_orderse8_gape8_gap_profilee8_gape8_gap_tablee8_gapE8_icgroupsE8_lusztig_map_ellipticexceptionalNilpotentDataE8_namesspringer_table_E8E8_nilpotent_dataexceptionalNilpotentDataE8_nilpotent_orbit_dual_mapspringer_table_E8E8_qgroupsE8_q_dataE8_q_unipdataE8_sgroupsE8_s_dataE8_s_unipdataE8_specialspringer_table_E8E8_Springer_mapspringer_table_E8E8_Springer_table_dataspringer_table_E8easy_factorsnumber_theoryech_upmatrixed_verboseext_deformedge_sequencecombinatoricsEigenPairtype, good_W_representativeseigenpairsgood_W_representatives ×2eigenspace_dimensionsnilpotent_orbitseigenvaluesgood_W_representatives ×2eigenvectorgood_W_representativeseigenvectorsgood_W_representativeselementcyclotomicelements_of_centercenterelements_of_center_derivedcenterelements_of_fundamental_groupcentereliminate_duplicatesnilpotent_posetsellVogan-dualelliptic_conjugacy_class_repsellipticelliptic_simpleellipticelliptic_simple_decompositionW_classeselliptic_W_GraphW_orderEllipticDatumtype, exceptionalelliptics_for_standard_LeviellipticEllipticTabletype, exceptionalembedcyclotomic · character_table_reps ×3 · cyclotomic_Lie_algebra · cyclotomicMat · bracketembed_affnilpotent_orbitsembed_coxetersubgroupsembed_coxeterssubgroups ×2embed_KGBparabolics · inductionembed_leftcomplexembed_simple_reflectioncharacter_table_repsempty_setfield ofLinearSolution, basicentryratmatenumerate_classnew_conjugacyenumerate_classesnew_conjugacyepsilonstructure_constantsepsilon_icoherent_characters ×4epsilon_rcoherent_characters ×2eqfield ofHashInfo, hashequalposet · springer_tablesequal_central_invariantgalois ×2equal_subgroupsgeck_genericequivalence_class_ofparabolicsevalpolynomial ×5 · KL_polynomial_matriceseval_at_modhasheval_char_Tweyl_character_formulaevaluate_at_1stable ×2 · polynomial ×3 · hodgeParamPolevaluate_at_shodgeParamPoleven_dual_orbitsnilpotent_orbitseven_eigenspacesnilpotent_orbitseven_orbitsnilpotent_orbits ×2even_placescombinatoricsexact_dividebasicexceptional_elliptic_centr_orderellipticexceptional_elliptic_char_polysellipticexceptional_elliptic_class_orderellipticexceptional_elliptic_conjugacy_class_ordersellipticexceptional_lusztig_maps_ellipticexceptionalNilpotentDataexceptional_nilpotent_tablesexceptionalNilpotentDataexchange_long_shortisomorphism_Wexchange_long_short_indexisomorphism_Wexhausthashexp_1cyclotomicexp_2basicexp_comp_inverseexp-generating-seriesexp_diffexp-generating-seriesexp_divideexp-generating-seriesexp_multexp-generating-seriesexp_multiplyexp-generating-seriesexp_of_exponential_seriesexp-generating-seriesexp_sbasicexp_substituteexp-generating-seriesexpandnumber_theory · K_types ×2exportsub_cells · weak_packetsext_basicextendedext_blockextended ×3ext_block_ofextended ×3ext_lengthextended_types ×2ext_powerW_classes · character_tablesext_print_blockextended ×3ext_typeextended_types ×2ext_type_1extended_typesext_type_2extended_typesext_type_3extended_typesext_typesextended_typesextendlazy_listsextend_0lazy_listsextend_LeviLevi_subgroupsextended_status_textsbasicExtParamtype, extended_miscExtParamPoltype, extParamPolextParamPolextParamPol ×2extract_nodessub_cellsextract_stringsW_reps_type_BC
F
Fgood_W_representatives · field ofCyclotomicFieldElement, cyclotomic · cyclotomic_Lie_algebra · cyclotomicMat ×2ffield ofhodge_function, hodge_functionsF4lietypesF4_B4groupsF4_cgroupsF4_elliptic_wordsellipticF4_icgroupsF4_lusztig_map_ellipticexceptionalNilpotentDataF4_namecharacter_table_FF4_nilpotent_dataexceptionalNilpotentDataF4_nilpotent_orbit_dual_mapspringer_table_FF4_sgroupsF4_s_dataF4_s_unipdataF4_spherical_unitaryunitaryF4_Springer_mapspringer_table_Ffactor_actionW_Kfactor_scalarmatrixfactor_strongWeylgroupfactorialbasicfactorizationnumber_theoryfactorsbasic · Weylgroupfailfield ofOne_of, basicfailedK_Nilpotentfailed_avK_Nilpotentfailed_av_annK_Nilpotentfailsbasicfalling_powercombinatoricsfamiliesfamiliesfamilyfamilies ×2fd_onlyfinite_dimensionalfd_reportfinite_dimensional_signaturefd_report_tracefinite_dimensional_signaturefgrepbasicfiberL_packet ×2fiber_partitionmiscFibonaccilazy_listsfig_verbosespecial_repfillK_Nilpotent ×2 · hashfill_nilpotent_posets_minimalnilpotent_posetsfill_nilpotent_posets_subregularnilpotent_posetsfill_one_stepK_Nilpotentfill_outhodge_K_type_formulafill_out_recursivelyhodge_K_type_formulafill_structure_constant_tablestructure_constantsfilterbasic · nilpotent_orbits · subgroupsfilter_by_classsubgroupsfilter_maxW_reps_type_BCfilter_weaksubgroupsfinalK_highest_weightsfinal_subsetKL_polynomial_matricesFinalizemiscfinalizemisc ×2findbasic ×7 · tits_centralizer · nilpotent_orbits ×2 · cells · K_types · hodgeParamLaurentPol · extended · disconnected · nilpotent_posets · K_types_plusfind_all_conjugatesubgroupsfind_cayleynilpotent_orbitsfind_classgaloisfind_conjugatenilpotent_orbits · subgroupsfind_Hnilpotent_orbitsfind_inbasicfind_induced_genericspecial_repfind_Levigeck_genericfind_Ninduction ×2find_nci_rootK_highest_weightsfind_posrootsyntheticfind_ratvec_mod_vecweyl_character_formulafind_vecnilpotent_orbitsfind_weaksubgroupsfind_x_with_dominant_rho_cK_highest_weights ×2finite_center_stringcenterfinite_dimensionalfinite_dimensional · representationsfinite_dimensional_fundamental_weight_coordinatesrepresentationsfinite_quotientlatticefirstbasic ×5 · sommers ×2first_columnslatticefirst_K_typebasicfirst_parambasicfirst_rowslatticefirst_set_bitbasicfirst_unset_bitbasicfive_inner_productsfour ×3five_inner_products_rfour ×2fix_addpolynomialfix_subpolynomialfixedextended_miscfixed_blockextended_miscfixed_block_ofextended_miscfixed_involutionscoherent_characters ×2fixed_kgbcoherent_charactersfixed_liftVogan-dualfixed_paramscoherent_charactersfixed_subsetbigMatricesflattenmiscfloorbasicfoldedtwisted_root_datum ×2folded_bracketextendedfolded_mextendedfolded_orderextendedfolding_orderaffinefolding_ordersaffinefoldlgenericsfoldrgenericsfor_allbasicfor_dual_datumbasicfor_nonebasicfor_somebasicform_namebasicformatcyclotomic · polynomial ×2 · extended_misc · cyclotomicMat · bracketforward_differencesbasicfour_inner_productsfourfree_quotient_lattice_basislatticefreq_test_Bspringer_table_BCfreq_test_Cspringer_table_BCfreq_test_Dspringer_table_DfrequenciescombinatoricsFrobenius_Schurfinite_dimensional_signaturefrom_core_quotient_2combinatoricsfrom_dlambda_domWeylgroupfrom_dominantbasic ×6from_dominant_rootbasicfrom_no_CminusWeylgroup ×2 · Levi_subgroups ×2from_no_CplusWeylgroup ×2 · Levi_subgroups ×2from_simpleWeylgroupfrom_standard_LeviLevi_subgroupsfrom_stopsbasicfsfinite_dimensional_signaturefstfield ofPair, basicfull_bitsetbasicfull_deformbasic · extParamPolfull_KL_inverse_mat_at_1klfull_signed_KL_mat_at_1klfull_solveGaussian_elim · cyclotomic_Gaussian_elimfunctions_on_real_orbitK_Nilpotentfundamental_Cartanbasicfundamental_coweightsbasicfundamental_groupcenterfundamental_weight_coordinatesfinite_dimensional · K_highest_weightsfundamental_weightsbasicfundamental_weights_K_HK_highest_weights
G
GG2_unitary_dualgfield ofExtParam, extended_misc · laurentPolynomial · nilpotent_posetsG2lietypesG2_cgroupsG2_class_wordsclass_tablesG2_elliptic_wordsellipticG2_icgroupsG2_lusztig_map_ellipticexceptionalNilpotentDataG2_nilpotent_dataexceptionalNilpotentDatag2_parameterG2_unitary_dualG2_sgroupsG_K_roots_and_corootsKG_K_roots_and_coroots_rawKg_parametercomplexGalois_actioncyclotomicGalois_matricescyclotomicGalois_matrixcyclotomicgammafield ofExtParam, extended_miscgamma_Lcomplexgamma_lG2_unitary_dualgamma_Rcomplexgamma_sG2_unitary_dualGAP_positions_E8character_table_E8gap_power_2e8_gapgap_power_3e8_gapgap_power_5e8_gapgap_power_7e8_gapGAP_reorder_E8character_table_E8gcdbasic ×2gcd_Bezout_coefnumber_theorygcd_bigbasicgenerateW_orbit ×2generate_action_from_domW_orbitgenerate_all_binarymiscgenerate_all_subsetsmisc ×3generate_from_domW_orbitgenerators_of_component_groupnilpotent_orbitsgenerators_of_component_group_debugnilpotent_orbitsgenerators_of_component_group_oldnilpotent_orbitsgenerators_of_Z_mod_Z_0nilpotent_orbitsgeneric_degreecharacter_tables · springer_tablesgeneric_degreesgeck_generic ×2 · generic_degrees ×2geometric_progressionlazy_listsgetfield ofIterator, basicget_dataall_finite_order ×2 · Gaussian_elim · cyclotomic_Gaussian_elimget_firstbasic ×2get_lastbasic ×2get_raw_dataall_finite_orderget_subsetsall_finite_orderget_subsets_given_orderall_finite_orderget_ystablegg_verbosegeck_genericGK_dimassociated_variety_annihilatorGK_dim_maximal_idealassociated_variety_annihilator ×2GLgroups ×2GL_CgroupsGL_HgroupsGL_partsommers ×2GL_RgroupsGL_rootsgroupsgood_datatype, weyltosemisimplegood_infogood_W_representatives ×2good_reportgood_W_representatives ×2goodnessinduction ×3gp_alg_eltcomplexgp_alg_elt1complexgraded_composition_seriesjantzen ×3graded_multiplicityjantzen ×3graded_standardjantzen · coherent_irreduciblegrading_coweightsyntheticgraphfield ofWCell, W_reps · poset ×4 · exceptional ×3 · nilpotent_posetsgraph_actionW_reps ×3graph_Hecke_actioncoherent_irreducible ×2graph_Hecke_action_columncoherent_irreduciblegraph_Hecke_irr_actioncoherent_irreduciblegraph_Hecke_irr_action_columncoherent_irreduciblegreaterposetgreedyGaussian_elim · cyclotomic_Gaussian_elimgroup_by_conjugacysubgroups ×2group_by_number_simple_factorssubgroupsgroup_by_rhosubgroupsgroup_by_ss_ranksubgroupsgroup_by_ss_rank_and_number_simple_factorssubgroupsgroup_parameters_by_primitive_idealprojectors_using_character_tablesgroup_parameters_projectionprojectors_using_character_tablesgroup_vectors_up_to_scalarprojectors_using_character_tablesgroup_vectors_up_to_scalar_altprojectors_using_character_tablesgroupscoherent_charactersgrowthGK_dimensiongrowth_irrGK_dimensiongrowth_stdGK_dimensionGSpgroups ×2GSp_CgroupsGSp_HgroupsGSp_Rgroups
H
Hgroups · field ofComplexNilpotent, nilpotent_orbits · field ofRealNilpotent, nilpotent_orbits · field ofComplexNilpotent_d, disconnected · cyclotomic_Lie_algebra ×2 · bracket ×2 · exceptionalhlaurentPolynomialH1galois · G2_unitary_dualH2G2_unitary_dualH_candidatesnilpotent_orbitsh_form_branch_irrc_form_branchh_form_branch_stdc_form_branchh_initcoherent_irreducibleH_lG2_unitary_dualH_sG2_unitary_dualh_testcoherent_irreducible ×2halfbasic ×4has_all_generic_degreesgeck_generichas_connected_centerbasichas_cyclic_centercenterhas_generic_degreegeck_generichas_infinitesimal_charactermodules · stablehas_theta_stable_LeviparabolicsHashtype, hashhash_codefield ofHashInfo, hash · hash ×10 · W_classesHashInfotype, hashhc_parameterrepresentations ×2He_testerW_classesHe_witnesserW_classesheadfield ofinfinite_node, lazy_listsheightbasic ×2 · misc ×2height_splitbasic ×2hermitian_dualhermitianhermitian_form_irreduciblehermitian ×3hermitian_form_irreducible_bigextParamPolhermitian_form_irreducible_longhermitian ×2hermitian_form_is_purehermitianhermitian_form_stdhermitianhexadecimalbasichighest_coroot_indicesbasichighest_corootsbasichighest_rootbasichighest_root_indicesbasichighest_rootsbasichighest_short_rootaffinehighest_short_rootsaffinehighest_weightK_highest_weights ×3highest_weight_finite_dimensionalfinite_dimensionalhighest_weight_finite_dimensional_ratvecfinite_dimensionalhighest_weight_oneK_highest_weights ×2highest_weight_split_sphericalK_highest_weights ×4highest_weightsK_highest_weights ×4Hn_reptype, W_reps_type_BChodge_branch_irrhodge_K_type_formulahodge_branch_stdhodge_K_type_formula ×3hodge_compresshodge_deformhodge_deformation_termshodge_deformhodge_formula_irrhodge_K_type_formulahodge_functiontype, hodge_functionshodge_function_stdhodge_K_type_formula · hodge_tensorhodge_functions_verbosehodge_functionshodge_grading_irreduciblehodge_deformhodge_grading_stdhodge_deform ×2hodge_K_type_formulahodge_K_type_formulahodge_K_type_formula_debugginghodge_K_type_formulahodge_K_type_formula_oldhodge_K_type_formulahodge_K_type_formula_verbosehodge_K_type_formulahodge_K_type_mathodge_K_type_formula ×2hodge_K_type_mat_longhodge_K_type_formula ×2hodge_K_type_mat_trivialhodge_K_type_formulaHodge_K_type_polhodgeParamPol ×2hodge_K_type_polhodgeParamPolhodge_normalizehodge_normalize ×2hodge_normalize_0hodge_normalize ×2hodge_normalize_verbosehodge_normalizehodge_P_matrixhodge_deformhodge_param_laurent_polhodgeParamLaurentPol ×3hodge_param_polhodgeParamLaurentPol · hodgeParamPolhodge_printhodgeParamPol ×3hodge_print_longhodgeParamPol ×3hodge_recursive_deformhodge_deform ×3hodge_recursive_deform_reversehodge_deformhodge_reflectionhodge_normalize ×2hodge_reflection_complexhodge_normalizehodge_reflection_imaginaryhodge_normalizehodge_signed_P_matrixhodge_deformhodge_tablehodge_K_type_formulahodge_tensorhodge_tensor ×2hodge_tensor_exterior_u_cap_shodge_tensorhodge_tensor_exterior_u_cap_s_stdhodge_tensor ×2hodge_tensor_stdhodge_tensor ×5hodge_tensor_wedge_k_u_cap_shodge_tensorhodge_tensor_wedge_k_u_cap_s_stdhodge_tensor ×2hodge_testhodge_test ×3hodge_test_verbosehodge_testhodge_theta_induce_standardhodge_functions ×2hodge_verbosehodge_deformHodgeKTypePoltype, hodgeParamPolhodgeParamLaurentPoltype, hodgeParamLaurentPolhodgeParamPoltype, hodgeParamPolhodgePrinthodge_functionshodgePrintPolyMatrixhodge_K_type_formula ×2hook_lengthW_reps_type_BChook_lengthscombinatorics ×2hppfield ofhodgeParamLaurentPol, hodgeParamLaurentPolhtfinite_dimensionalhyperoctahedral_charactercombinatorics
I
Igenerics · modulesi_laurent_polytype, laurentPolynomiali_MG2_unitary_duali_polytype, polynomiali_poly_mattype, polynomialI_will_survivetranslateicfield ofExtParam, extended_miscicrosscoherent_irreducible ×3icross_gradedcoherent_irreducibleid_classcharacter_tablesid_matcyclotomicMatid_Wbasicidentity_in_fund_domainall_finite_orderidentity_poly_matrixpolynomialidentity_rowbasicimagebasic · field ofStdLeviEltImage, W_classesimage_complement_basislatticeimage_latticelatticeimage_projectorlatticeimage_subspacelatticeimaginary_corootsbasicimaginary_poscorootsbasic ×2imaginary_posrootsbasic ×2imaginary_rootsbasicimaginary_roots_and_corootsbasic ×2imaginary_sysbasic ×2imaginary_typebasic ×2 · hodge_normalizein_Aextended_miscin_distinguished_fiberbasicin_fppG2_unitary_dual ×3in_fundamental_alcoveaffine ×2in_latticelattice ×2in_lattice_basislatticein_lattice_subspace_sumlatticein_one_plus_delta_Zgaloisin_radicalnilpotent_orbitsin_spanK_Nilpotent ×2in_string_listbasicin_taumodules · stable ×2 · sub_cellsin_tau_complementmodules · stable ×2include_Q_and_P_X_matricesfield ofKNilpotentData, K_Nilpotentinclusion_maximalsW_reps_type_BCincrfield ofIterator, basicind_verboseinductionindeterminatefield ofint_poly, polynomial · field ofrat_poly, polynomialindexfinite_dimensional_signature · field ofHash, hash · character_tablesindex_BC_irrepclassical_character_tablesindex_bipartitioncombinatoricsindex_D_classescombinatoricsindex_D_irrepsclassical_character_tablesindex_D_repsclassical_W_classes_and_reps ×2index_inbasic ×3index_long_reflectioncharacter_tablesindex_partitioncombinatoricsindex_short_reflectioncharacter_tablesindex_standard_basisisomorphism_Windex_stringfinite_dimensional_signatureindex_tracefinite_dimensional_signatureindex_trace_stringfinite_dimensional_signatureindicesbasic · stableindices_subsetbigMatricesindsK_highest_weightsinds_plusK_types_plusinducespecial_repinduce_characterW_reps · character_table_reps ×9induce_from_gen_parabolic_irrinductioninduce_multiplenilpotent_inductioninduce_orbittruncated_induction ×3induce_signcharacter_table_reps ×2induce_trivialcharacter_table_reps ×2induced_bijection_on_classesisomorphism_Winduced_permutation_on_classesisomorphism_Winduced_unipotentsweak_packetsinduced_unipotents_longweak_packetsinf_chars_dom_for_Laqlinf_chars_for_Laql ×2inf_listtype, lazy_listsinf_nodetype, lazy_listsinf_oneslazy_listsinfinite_listtype, lazy_listsinfinite_nodetype, lazy_listsinfinitesimal_characterbasic ×2 · modules ×2 · sommersinfinitesimal_character_oldsommersinfoall_finite_order ×2info_reducedall_finite_orderinitiallazy_listsinitial_torus_factorgroup_operationsinitialize_KNilpotentK_Nilpotent ×4initialize_structure_constant_tablestructure_constants ×2inject_KK ×2injection_from_K_matrixK ×2innerfield ofWeylClassTable, W_classes · character_tablesinner_classbasic ×5 · field ofKGBElt_gen, syntheticinner_formsgroup_operationsinner_liftL_packet ×3inner_lift_stdL_packet ×4inner_productcharacter_tablesInnerClass_hashtype, hashint_formatbasicint_mappingisomorphism_Wint_partbasic · misc · K_typesint_polytype, polynomialintegral_change_basiscoordinates ×3integral_descentnilpotent_orbits · springer_tablesintegral_inverse_change_basiscoordinates ×3integral_shiftVogan-dualintegrality_datumbasic · nilpotent_orbits · extended_miscintegrality_rankbasicintegrally_dominantWeylgroupintegrally_from_dominantWeylgroupintersectcomplex · disconnectedintersectionsub_cells ×2 · latticeintersection_pluslatticeinv_factbasicinvariant_formWeylgroupinvariant_form_matrixWeylgroupinversebasic ×2 · combinatorics · ratmat · parameters · tits · affine · cyclotomic · Gaussian_elim · cyclotomic_Gaussian_elim · lazy_listsinverse_by_matrixcyclotomicinverse_by_normcyclotomicinverse_by_solvecyclotomicinverse_change_basiscoordinates ×3inverse_embed_KGBparabolics · inductioninverse_image_simple_factortwisted_root_datuminverse_make_coordstits_centralizerinverse_modnumber_theoryinverse_springer_Cspringer_table_BC ×2inverse_springer_partition_Bspringer_table_BCinverse_springer_partition_Cspringer_table_BCinversescomplexinvertibles_modulonumber_theoryinvolutionbasic ×3 · field ofKGBElt_gen, syntheticinvolutionscoherent_characters ×2irrmodulesirreducible_labelfield ofCharacterTable, character_tablesirreducibles_as_sums_of_standardsL_packetirrep_labelclassical_character_tablesis_abeliangroup_operationsis_adjointbasicis_affine_conjugateaffine ×2is_affine_dominantaffine ×2is_Aqnilpotent_orbits ×2is_Aq_cellnilpotent_orbitsis_ascentbasic ×3is_birigidsommersis_closedparabolicsis_coh_ind_from_finite_dimensionalinductionis_compactbasic ×3is_compact_imaginarybasic ×4is_compatiblebasicis_complexbasic ×4 · complex · sub_cellsis_conjugateall_finite_order · synthetic · nilpotent_orbitsis_conjugate_inW_classesis_conjugate_Kacall_finite_orderis_conjugate_orbitnilpotent_orbitsis_conjugate_pseudo_Levinilpotent_orbitsis_conjugate_weakconjugate ×2is_containedsubgroups ×2is_corootbasicis_defaultextendedis_descentbasic ×3is_disjointbasicis_disjoint_frombasicis_disjoint_from_sortedbasicis_distinguishedsommers · twisted_root_datum · exceptionalis_dominantbasic ×2is_doubly_evencombinatoricsis_dual_AqVogan-dual ×3is_dual_Aq_intVogan-dualis_dual_Aq_tempVogan-dualis_ellipticWeylgroupis_elliptic_for_LeviW_classesis_equal_rankbasicis_equivalentextended_miscis_evenbasic · nilpotent_orbits · exceptionalis_fairinduction ×3is_finalinductionis_finite_dimensionalfinite_dimensionalis_fixedsynthetic · extended_misc ×4is_fundamental_CartanKis_goodinduction ×3is_good_Aqinductionis_good_range_induced_frominductionis_hermitianhermitianis_imaginarybasic ×4is_in_class_ofparabolicsis_in_cross_orbitcross_W_orbitis_in_listinductionis_integerbasic ×2 · cyclotomicis_integralbasic ×2is_integrally_dominantbasic ×2is_isomorphicW_reps · lietypes · isomorphismis_LeviLevi_subgroups · subgroupsis_locally_isomorphiclietypesis_longWeylgroupis_maxW_reps_type_BCis_maximal_forparabolicsis_memberbasic ×5is_member_bitsetbasicis_member_fastbasicis_member_sortedbasicis_monotoneposetis_multiplicative_generatornumber_theory ×2is_negative_corootbasic ×2is_negative_rootbasic ×2is_negcorootbasicis_negrootbasicis_non_evennilpotent_orbitsis_non_negativepolynomial · bigMatrices ×2is_noncompactbasic ×2is_noncompact_imaginarybasic ×4is_nonnegativemisc ×2is_nonparitybasic ×2is_normalis_normal ×3is_normal_Kis_normal ×2is_not_less_singulartranslateis_oddbasicis_one_dimensionalinductionis_one_factoraffine ×2is_openparabolicsis_orthogonalbasic ×3is_P_positiveW_Kis_paritybasic ×2is_partitioncombinatoricsis_permutationcombinatoricsis_poscorootbasicis_positivecoherent_irreducible · misc ×2is_positive_corootbasic ×2is_positive_rootbasic ×2is_posrootbasicis_primenumber_theoryis_proper_Aqinductionis_proper_subsetmisc · parametersis_pseudo_Levisubgroupsis_pseudo_Levi_in_simplesubgroupsis_pseudo_Levi_in_simple_adjointsubgroupsis_purebasic ×4is_pure_1basic ×3is_pure_sbasicis_quasicompactbasicis_quasisplitbasicis_rationalcyclotomic · cyclotomicMatis_rational_multipleprojectors_using_character_tablesis_realbasic ×4 · cyclotomic · cyclotomicMatis_real_induced_from_character_from_Paqlis_real_induced_from_one_dimensionalaqlis_regularbasic ×3is_relatively_ellipticWeylgroupis_relatively_splitgroup_operationsis_rootbasicis_saturatedlatticeis_self_conjugatefinite_dimensional_signatureis_self_dualfinite_dimensional_signatureis_semisimplebasicis_semisimple_element_conjugatetwisted_conjugacy ×2is_semisimple_element_conjugate_in_semisimpletwisted_conjugacy ×2is_semisimple_element_conjugate_mod_torustwisted_conjugacy ×2is_shortWeylgroupis_simplebasic ×2 · affineis_simple_forbasicis_simple_rootmiscis_simply_connectedbasicis_solvable_for_torus_elementtits_centralizeris_sortedsortis_sorted_subsetW_reps_type_BCis_specialcombinatorics · springer_tables ×2 · W_reps_type_BC ×3 · exceptionalis_special_representationcharacter_tables ×2 · springer_tables ×2is_splitbasic ×2 · classical_W_classes_and_reps ×2is_split_sphericalK_highest_weights ×2is_stableL_packet · parabolicsis_stable_irrL_packetis_stable_stdL_packetis_standardinductionis_standard_Leviparabolicsis_strict_descentbasicis_strictly_complexcomplex · sub_cellsis_strictly_dominantbasic ×2is_strongly_compatibleK_types_plusis_strongly_regularbasicis_subsetbasic · parametersis_subset_ofbasicis_subset_of_sortedbasicis_substringbasicis_theta_xinductionis_unitaryhermitian ×2is_unitary_bigextParamPolis_unitary_by_casesaqlis_unitary_characterinductionis_unitary_reducedaqlis_unitary_reduced_with_formaqlis_unitary_sraqlis_validcombinatorics ×2 · L_packetis_very_evencombinatoricsis_W_conjugatenilpotent_orbitsis_w_conjugatenilpotent_orbitsis_W_conjugate_by_wnilpotent_orbits ×2is_weakly_fairinduction ×3is_weakly_fair_Aqaqlis_weakly_fair_Aq_from_Paqlis_weakly_goodinduction ×3is_weakly_good_Aqinductionis_weakly_unitaryhermitian ×2is_weakly_unitary_bigextParamPolis_wf_induced_from_one_dimaqlis_zeropolynomial · hodge_functionsisnt_memberbasic ×5isnt_member_bitsetbasicisnt_member_fastbasicisnt_member_sortedbasicisomorphismisomorphismisomorphism_longisomorphismiterate_H1galois ×3iterate_maximal_pseudo_Levissubgroupsiterate_maximal_pseudo_Levis_longsubgroupsIteratortype, basiciteratorhash
J
JmodulesJ_inducetruncated_induction ×2j_inducetruncated_induction ×2jacobi_formulastructure_constants · cyclotomic_Lie_algebra · bracketjacobi_identitiescyclotomic_Lie_algebra ×2 · bracket ×2jacobi_identities_longcyclotomic_Lie_algebra ×2 · bracket ×2jacobi_structure_constants_identitystructure_constants ×2jJ_inducetruncated_inductionjJ_select_inducetruncated_inductionJM_tripletits_centralizer ×2 · bracket ×5JM_triple_onetits_centralizerJM_triple_signsbracket ×7JM_triple_strongtits_centralizer ×3JM_triplestits_centralizer · bracket ×2JM_triples_signsbracket ×2joinbasic · springer_table_E8
K
KdisconnectedK0_paramK_highest_weights ×4K0_param_from_highest_weightK_highest_weightsK0_paramsK_highest_weights ×2K_0K ×3K_basisK_Nilpotent ×5K_basis_closureK_NilpotentK_basis_closure_of_real_orbitK_Nilpotentk_highest_weightKK_highest_weight_from_fundamental_weightsK_highest_weightsK_highest_weight_from_K0_weightK_highest_weightsK_intcomplexK_normK ×3 · K_norm ×10K_normsK · K_norm ×2K_parameters_height_uptoK_norm ×7K_parameters_norm_uptoK_norm ×3K_root_datumKK_signature_irrK_typesK_typeK_highest_weightsK_type_formulabasic · tensor_productK_type_formula_plusK_type_formulaK_type_formula_verboseK_type_formulaK_type_lambdabasicK_type_polbasicK_typesmodules · K_highest_weightsK_types_plusK_types_plus ×2Kac_classes_given_orderall_finite_orderKac_classes_given_order_crudeall_finite_orderKac_diagrams_with_centralizernilpotent_orbitsKac_diags_given_orderall_finite_orderKac_diags_of_identityall_finite_orderKac_diags_up_to_orderall_finite_orderKac_triplesnilpotent_orbitsKac_triples_simplenilpotent_orbitsKac_xall_finite_orderkeep_by_first_entryW_reps_type_BC ×2keep_by_first_entry_and_truncateW_reps_type_BC ×2keep_longrestricted_rootskeep_long_roots_short_corootsrestricted_rootskeep_shortrestricted_rootskeep_short_roots_long_corootsrestricted_rootskernelratmat · cyclotomic_Gaussian_elimkernel_vanishingstableKGBbasic ×2KGB_eltbasic ×3 · synthetic · parametersKGB_elt_gensynthetic ×2KGB_status_textbasicKGBElt_gentype, syntheticKGBratvectype, hashKGPparabolics ×2KGP_eltparabolicsKGP_elt_forparabolicsKGP_numbersparabolicsKGPElttype, parabolicsKHighestWeighttype, KKL_blockKL_polynomial_matricesKL_block_rawext_deformKL_inverse_mat_at_1klKL_P_polynomialsKL_polynomial_matrices ×4KL_P_polynomials_at_minus_oneKL_polynomial_matrices ×4KL_P_signed_polynomialsKL_polynomial_matrices ×4KL_P_signed_polynomials_at_minus_oneKL_polynomial_matrices ×4KL_Q_polynomialdualKL_Q_polynomialsKL_polynomial_matrices ×4kn_verboseK_NilpotentKNilpotentDatatype, K_NilpotentKondo_positionscharacter_table_Fkottwitz_invariantL_packetkottwitz_signL_packetkronecker_fmatrixkronecker_gmatrixKronecker_productmatrixkronecker_productmatrixKType_hashtype, hashKTypePol_hashtype, hash
L
Lfield ofother_entry, Levi_subgroupslfield ofExtParam, extended_miscl_adjustbasic · tabulateL_cap_K_basisK_Nilpotent ×3L_cap_K_basis_oppK_NilpotentL_dominant_conjugatesK_normL_infinitesimal_characterinductionL_intfield oforbit_entry, Levi_subgroupsL_packetL_packet ×2L_packet_representativeL_packetL_packet_representativesL_packet ×2L_packet_stable_sumL_packetL_packetsL_packetlabelsfield ofWCell, W_reps · affinelambdabasic ×2 · field ofKGBratvec, hash · parameters ×2lambda_minus_rhobasic ×2lambda_plus_rho_res_Tconvert_c_formlambda_rhobasic · field ofExtParam, extended_misclambda_rho_from_dominant_height_uptoK_norm ×2lambda_rho_from_dominant_norm_uptoK_highest_weightslarge_discrete_seriesrepresentations ×2large_fundamental_seriesrepresentations ×2large_symbolW_reps_type_BC ×2large_symbol_BW_reps_type_BClarge_symbol_CW_reps_type_BClarge_symbolsW_reps_type_BClastbasic ×5 · sommers ×2last_column_mat_poly_inversehodge_deformlast_K_typebasiclast_parambasiclaurent_poly_as_polylaurentPolynomiallaurent_poly_formatlaurentPolynomiallcmbasic ×2leading_principal_minormatrixleading_termsK · K_norm ×2leftcomplex ×2 · tits ×3left_cell_ofsub_cellsleft_cell_of_oldsub_cellsleft_cellssub_cellsleft_copysub_cellsleft_corootssub_cellsleft_factorssub_cellsleft_Gcomplex ×2left_inversematrix · ratmatleft_kernelstableleft_reflectbasic ×2left_rhocomplexleft_root_indicessub_cellsleft_rootssub_cellsleft_Wcomplex ×2left_wcomplexlengthWeylgroup · K · extended · field ofEllipticDatum, exceptionallength_signcoherent_irreduciblelengthensbruhat · Weylgroup ×2lengths_signsstable ×2lengths_signs_matrixstable ×2leq_by_numberparabolicsleq_E7_signaturesclass_tableslessposet · W_orderless_eqcombinatoricsLeviparabolics · field ofrho_data, Levi_subgroups · field ofStdLeviEltImage, W_classes · exceptionallevigood_W_representativesLevi_AcombinatoricsLevi_by_cwtparabolicsLevi_by_wtparabolicsLevi_coweightparabolicsLevi_datumLevi_subgroups ×3Levi_infoLevi_subgroups ×2Levi_lookupLevi_subgroups ×2Levi_normalizer_indexW_classesLevi_ofW_classesLevi_of_coweightsubgroupsLevi_of_dual_subspacesubgroupsLevi_of_Hnilpotent_orbitsLevi_of_orbitnilpotent_orbitsLevi_of_subspacesubgroupsLevi_of_wsubgroupsLevi_of_weightsubgroupsLevi_orbitW_classesLevi_orbit_sizeW_classesLevi_reducerW_classesLevi_reducer_classifyW_classesLevi_reducer_rhoW_classesLevi_reprfield ofStdLeviOrbit, Levi_subgroupsLevi_signatureW_reps_type_BCLevi_simple_corootsparabolicsLevi_simple_rootsparabolicsLevi_subgroupssubgroupsLevi_weightparabolicsLevi_witnessconjugateLeviConjugacyTestertype, W_classesLeviConjugacyWitnessertype, W_classesLeviInfotype, Levi_subgroupsLevis_with_distinguished_orbitnilpotent_orbitslex_leqsortlexicographicsortlie_algebra_elementcyclotomic_Lie_algebra ×2 · bracketlie_algebra_element_root_vectorscyclotomic_Lie_algebra ×2 · bracketlie_algebra_element_semisimplecyclotomic_Lie_algebra ×2 · bracketlie_compact_radicalcenterlie_compact_radical_hatcenterlie_coradical_partcenterlie_radicalcenterlie_radical_hatcenterlie_radical_partcenterlie_split_radicalcenterlie_split_radical_hatcenterLie_typebasicLieAlgebraElementtype, bracketlifthash · tits ×3 · center · nilpotent_orbits · disconnectedlift_actionW_Klift_scWeylgroupLinearSolutiontype, basiclinkssub_cellslistbasic · coherent_irreducible · field ofHash, hashLKTK_highest_weights ×2LKT_verboseK_highest_weightsLKTsK_highest_weights ×2local_isomorphismisomorphismlocal_isomorphism_longisomorphismlocate_sortedbasiclog_zextended_misc ×2log_zetaextended_misc ×2long_formatextended_misclong_nameexceptional ×2long_rat_as_integer_stringfinite_dimensional_signaturelookupbasic · hodge_K_type_formula · hash · structure_constantslookup_by_alt_nameexceptionallookup_by_diagramexceptionallookup_by_nameexceptional ×2lookup_character_tablegeck_genericlookup_character_table_oldgeck_genericlookup_columnbasiclookup_insortlookup_rowbasiclowerbasic ×2lower_unitriangular_inversepolynomiallowest_corootsbasiclowest_powerlaurentPolynomiallowest_rootsbasicLusztig_cellcoherent_characterslusztig_celllusztig_cells ×2lusztig_cell_classicalW_reps_type_BC ×2lusztig_cell_longlusztig_cellslusztig_cell_pluslusztig_cellsLusztig_cellscoherent_characterslusztig_cellslusztig_cells ×3lusztig_cells_classicalW_reps_type_BClusztig_cells_pluslusztig_cellslusztig_graphexceptionallusztig_of_special_ellipticnilpotent_posets ×2
M
MG2_unitary_dualmnilpotent_centralizer · test_braidm_0nilpotent_centralizerm_2nilpotent_centralizerm_minusstructure_constants ×2m_parametercomplexm_plusstructure_constants ×2Magma_positions_E6character_table_E6Magma_positions_E7character_table_E7main_diagonalbasicmain_diagonal_square_blockmatrixmake_blockcoherent_charactersmake_coordstits_centralizermake_dominantinductionmake_dominant_Hnilpotent_orbitsmake_dominant_using_rootsWeylgroup ×2make_hashhashmake_InnerClass_hashhashmake_inverseGaussian_elim · cyclotomic_Gaussian_elimmake_KGBsyntheticmake_KType_hashhashmake_KTypePol_hashhashmake_mat_hashhashmake_parabolicparabolics · inductionmake_Param_hashhashmake_param_polstablemake_ratvec_hashhashmake_RealForm_hashhash ×2make_regularstable · parametersmake_regular_paramtranslatemake_RootDatum_hashhashmake_specialcombinatorics ×3make_strongly_compatible_parabolicK_types_plusmake_strongly_dominantW_K · K_highest_weightsmake_vec_hashhashmake_vectorfour ×2make_W_elementgood_W_representativesmake_xlambda_hashhashmakeSparabolics ×2 · induction ×2 · nci_nilrad_rootsmapbasic ×7 · hermitianmap_characterisomorphism_Wmap_into_distinguished_fiberinductionmap_onbasicmap_root_of_unitytits_centralizer ×2map_to_centercentermaster_complex_nilpotent_posetnilpotent_posetsmat_as_poly_matstable · polynomial · hodge_deformmat_as_ratmatratmatmat_hashtype, hashmatchhashmatrixbasic ×2 · ratmatmatrix_assignbasicmatrix_of_inner_productsW_repsmatrix_of_multiplicationcyclotomicmaxbasic ×7 · parabolicsmax_eigenvaluenilpotent_orbitsmax_first_entryW_reps_type_BCmax_heightbasic ×2 · miscmax_Hn_repW_reps_type_BC ×2max_Hn_repsW_reps_type_BCmax_initbasicmax_Levi_subgroupsgeck_genericmax_listbasicmax_locbasic ×2max_onlynilpotent_orbits · W_reps_type_BCmax_standard_Levi_conjugacy_representativesgeck_genericmax_tagged_entryW_reps_type_BCmaxdexbasicmaxima_forparabolicsmaximalparabolicsmaximal_central_torusgroup_operations ×2maximal_parabolicsparabolicsmaximal_pseudo_Levissubgroupsmaximal_pseudo_Levis_simplesubgroupsmaximal_real_parabolicsparabolicsmaximal_theta_parabolicsparabolicsmaximize_LeviLevi_subgroupsMaybetype, basicmaybe_conjugate_strictconjugatemaybe_inducetype, nilpotent_inductionmaybe_KTPtype, hermitianmemo_1_rdcharacter_tablesmemoizelazy_listsmergesort ×2 · nilpotent_posetsmerge_bysortmerge_matricesK_Nilpotent · matrixmerge_P_X_matricesK_Nilpotentmerge_T_matricesK_Nilpotentmerge_usort ×4merge_u_bysortmiddlesommers ×2millers_crossingcoherent_irreducible ×2millers_crossing_singcoherent_irreducible ×2minbasic ×7 · parabolicsmin_heightbasic ×4min_initbasicmin_listbasicmin_locbasic ×2mindexbasicminima_HeW_classesminimal_extendersLevi_subgroupsminimal_nodesposetminimal_orbit_simplenilpotent_orbitsminimal_orbitsnilpotent_orbitsminimal_principal_seriesrepresentations ×2minimal_real_Leviparabolicsminimal_real_nilpotent_orbitsnilpotent_orbitsminimal_real_parabolicparabolicsminimal_representativeW_classes ×2minimal_representative_with_witnessW_classes ×2minimal_representativesW_classesminimal_representatives_with_witnessW_classesminimal_spherical_principal_seriesrepresentations ×2minus_1basicminus_vee_to_the_khodge_functionsmixedhermitianmixed_radix_nrbasicmixed_radix_wordbasicmixed_termshermitianmod_central_torusbasic · group_operationsmod_image_projectorlatticemodified_cardinalityK_type_formulamonic_dividepolynomial ×3monomialbasic ×4monomialsbasic ×6 · hodgeParamLaurentPol ×2 · is_normalmost_split_Cartanbasicmove_by_Leviconjugatemove_P_down_by_Ninductionmove_to_distinguished_fibernilpotent_orbits ×3move_weightW_Kmucoherent_irreducible ×2 · field ofKHighestWeight, K · convert_c_form ×3mu_Ccomplexmu_termsconvert_c_formmultweak_packets ×3mult_blockweak_packetsmult_irrK_typesmult_orbit_blockweak_packetsmult_stdK_typesmulti_choosecombinatoricsmultinomcombinatoricsmultiplicitybasic · sommersmultiplicity_functiontype, hodge_functionsmultiplytits · lazy_listsmultiply_bylazy_listsmultiset_permutationscombinatoricsMurnaghan_Nakayamacombinatoricsmy_extended_blockbigMatricesmy_simple_rootsG2_unitary_dualmysortall_finite_order
N
Nfield ofKNilpotentData, K_Nilpotent · tensor_product · structure_constantsnfield ofphi_data, number_theory · field ofi_laurent_poly, laurentPolynomialn_classesW_classes · character_tablesn_columnsbasic · ratmat · cyclotomicMatn_irrepscharacter_tablesn_orbitsspringer_tablesn_partitionslazy_listsn_rowsbasic · ratmat · cyclotomicMatnamefield ofgood_data, weyltosemisimple · field ofEllipticDatum, exceptional · field ofNilpotentDatum, exceptionalname_to_diagram_E8springer_table_E8nc_verbosenew_conjugacynci_nilrad_roots_restricted_to_H_thetanci_nilrad_roots ×2negative_systembasicnegative_termscertificatenested_Levisgood_W_representativesnested_Levis_to_semisimplegood_W_representativesnew_block_linesyntheticnew_linebasicnew_ordertits_centralizernice_choice_xW_Knice_choices_xW_Knice_classesall_finite_ordernice_formatlietypes ×2nilpotentnilpotent_orbitsnilpotent_lambdasnilpotent_orbits_exceptionalnilpotent_lambdas_classicalnilpotent_orbit_partitionsnilpotent_lambdas_Enilpotent_orbits_exceptionalnilpotent_lambdas_E6nilpotent_orbits_exceptionalnilpotent_lambdas_E7nilpotent_orbits_exceptionalnilpotent_lambdas_E8nilpotent_orbits_exceptionalnilpotent_lambdas_F4nilpotent_orbits_exceptionalnilpotent_lambdas_G2nilpotent_orbits_exceptionalnilpotent_orbit_Aspringer_table_Anilpotent_orbit_Bspringer_table_BCnilpotent_orbit_Cspringer_table_BCnilpotent_orbit_Dspringer_table_Dnilpotent_orbit_GLspringer_table_Anilpotent_orbit_partitionsnilpotent_orbit_partitions ×2nilpotent_orbit_semisimple_elementsnilpotent_orbit_partitions ×2nilpotent_orbit_SOspringer_table_BC · springer_table_Dnilpotent_orbit_Spspringer_table_BCnilpotent_orbitsnilpotent_orbits · disconnectednilpotent_orbits_and_closuresnilpotent_posetsnilpotent_orbits_and_closures_inducenilpotent_posetsnilpotent_orbits_and_closures_saturatenilpotent_posetsnilpotent_orbits_and_closures_testnilpotent_posetsnilpotent_orbits_data_longshow_nilpotent_orbitsnilpotent_orbits_data_very_longshow_nilpotent_orbitsnilpotent_posetexceptional · nilpotent_posetsnilpotent_verbosenilpotent_orbitsNilpotentDatumtype, exceptionalNilpotentPosettype, nilpotent_posetsNilpotentTabletype, exceptionalnilradparabolics ×2nilrad_by_cwtparabolicsnilrad_by_wtparabolicsnilrad_rootsparabolics ×2nilrad_roots_by_cwtparabolicsnilrad_roots_by_wtparabolicsno_Cminus_rootsbasicno_Cplus_rootsbasicno_Cyclotomic_solutionfield ofCF_lin_solution, cyclotomic_Gaussian_elimno_F_factorisomorphism_Wno_orbitfield ofmaybe_induce, nilpotent_inductionno_pivotfield ofPivot_info, Gaussian_elim · field ofCyclotomic_Pivot_info, cyclotomic_Gaussian_elimno_repsbasic ×2nodesfield ofWGraph, W_repsnon_dominant_simplesbasic ×2non_even_dual_orbitsnilpotent_orbitsnon_even_orbitsnilpotent_orbits ×2non_integrally_dominant_simplesbasicnoncompact_posrootsbasicnondegenerate_invariant_formWeylgroupnonefield ofMaybe, basic · basic ×5nonparity_poscorootsbasicnormcyclotomicnorm2field ofWeylClassTable, W_classes · character_tablesnormalizecombinatorics · laurentPolynomialnormalizersubgroups ×2 · conjugatenormalizer_classesconjugatenormalizer_iteratorconjugatenormalizer_reportsubgroupsnormalizer_reportssubgroups ×2not_a_rootmisc ×2nubasic · parameters ×2 · extendednu_Ccomplexnullall_finite_order · cyclotomic_Lie_algebra · cyclotomicMat ×3 · bracketnull_ext_moduleextParamPolnull_K_modulebasic ×2null_modulebasic ×4null_poly_matstablenullHodgeFunctionhodge_functionsnullHodgeKTypePolhodgeParamPolnullHodgeParamLaurentPolhodgeParamLaurentPolnullHodgeParamPolhodgeParamPolnumberbasic ×2number_conjugacy_classes_Anilpotent_orbitsnumber_conjugacy_classes_component_groupnilpotent_orbitsnumber_factorsaffinenumber_K_parameters_norm_uptK_normnumber_K_parameters_norm_uptoK_normnumber_real_nilpotent_orbitsnilpotent_orbits ×6number_real_nilpotent_orbits_correct_central_invariantshow_nilpotent_orbitsnumber_real_orthogonal_pairsconvert_c_formnumber_simple_factorssimple_factorsnumber_unipotentsfinite_unipotentsnumber_unipotents_BCfinite_unipotentsnumber_unipotents_Dfinite_unipotentsnumber_unipotents_guessweak_packetsnumber_unipotents_simplefinite_unipotentsnumerbasic ×2
O
odd_eigenspacesnilpotent_orbitsodd_part_partitionscombinatoricsodd_placescombinatoricsomegafield ofExtParam, extended_miscomega_Lgeck_genericOmega_S_inversehodge_tensoron_fundamental_weightsfinite_dimensionalonecyclotomicone_dim_params_gammaaqlone_dim_real_induced_paramaqlone_dim_real_induced_param_polaqlone_minus_sbasicone_minus_vhodgeParamPolOne_oftype, basicone_plus_sbasiconesbasicoperatorW_reps ×2 · new_conjugacy ×2operatorsfield ofW_rep, W_reps · field ofWCell, W_reps · new_conjugacy ×6Orbittype, W_reps_type_BCorbitfield ofrho_data, Levi_subgroups · field ofComplexNilpotentComponentDatum, nilpotent_orbits · springer_tables · W_reps_type_BC ×4 · exceptional · field ofmaybe_induce, nilpotent_inductionorbit_BW_reps_type_BCorbit_CW_reps_type_BCorbit_closuresfield ofNilpotentPoset, nilpotent_posetsorbit_datatype, Levi_subgroupsorbit_entrytype, Levi_subgroupsorbit_indexspringer_tablesorbit_symbolssommers ×2orbit_symbols_Bsommersorbit_symbols_Csommersorbitsnilpotent_orbits · field ofSpringerTable, springer_tables · disconnected · field ofNilpotentPoset, nilpotent_posetsorbits_and_unipotentsfinite_unipotentsorbits_and_unipotents_strictfinite_unipotentsorbits_tableLevi_subgroupsOrbitSymboltype, sommersorderbasic ×2 · all_finite_order · field ofEigenPair, good_W_representatives · tits · field ofCyclotomicField, cyclotomic · cyclotomic · extended · field ofEllipticDatum, exceptionalorder_centercenterorder_in_Anilpotent_orbitsorder_of_centralizer_elliptic_BCDellipticorder_twisttwisted_root_datumorder_WWeylgroup ×2 · field ofWeylClassTable, W_classes · character_tablesorder_W_simpleWeylgroup ×2ordersfield ofComplexNilpotentComponentDatum, nilpotent_orbitsorientation_functionstructure_constants · field ofStructureConstantTable, structure_constantsorientation_nr_termbasicorth_reflectionratmatorthogonal_subgroupsubgroups ×2other_entrytype, Levi_subgroupsother_real_formsK_Nilpotentothersfield ofStdLeviOrbit, Levi_subgroupsout_listfield ofWNode, W_reps
P
psommersP_indfield ofExtParamPol, extParamPolp_lG2_unitary_dualP_matricesbigMatricesP_minusfield ofExtParamPol, extParamPolp_NinductionP_plusfield ofExtParamPol, extParamPolP_positive_test_coweightW_KP_positive_test_coweightsW_Kp_sG2_unitary_dualP_X_matricesK_Nilpotentpackets_disjointweak_packetspadbasic ×2 · tabulate · hodgeParamLaurentPolPairtype, basicpairsfield ofKNilpotentData, K_Nilpotent · field ofgood_data, weyltosemisimple · field ofComplexNilpotentComponentDatum, nilpotent_orbitspairs_of_total_sumcombinatoricsParabolictype, parabolicsparabolic_by_cwtparabolicsparabolic_by_cwt_verboseparabolicsparabolic_by_wtparabolicsparabolic_by_wt_verboseparabolicsparabolic_is_realparabolicsparabolic_is_theta_stableparabolicsparabolic_LKTK_highest_weightsparabolic_of_orbitnilpotent_orbitsparabolicsparabolics ×2parabolics_with_theta_stable_Leviparabolicsparamfield oftag_Param, modules · miscParam_hashtype, hashparam_polbasic ×2 · parameters ×2parameterbasic ×2 · L_packet · K · parameters ×2 · extended_miscparameter1_wcomplexparameter_gcomplexparameter_gammabasicparameter_mcomplexparameter_wcomplexparametersstable · cells ×3 · weak_packets ×3parameters_given_AVcellsparameters_given_AV_infinitesimal_charactercells ×3parameters_mapweak_packets ×2parameters_singularstableparameters_tau_contained_in_complementstableparameters_tau_containingstableparityparametersparity_poscorootsbasicparity_restricted_partitionscombinatoricspart_containinggaloispart_mults_to_classical_Hspringer_table_BCpart_restricted_partitionscombinatoricsPartitiontype, combinatoricspartition_as_irrep_labelclassical_character_tablespartition_bysortpartition_of_orbit_Bspringer_table_BCpartition_of_orbit_Cspringer_table_BCpartition_of_orbit_Dspringer_table_Dpartition_pairscombinatoricspartition_sumsommerspartitionscombinatoricspartitions_all_even_partssommerspartitions_all_odd_partssommerspartitions_Bspringer_table_BCpartitions_Cspringer_table_BCpartitions_Dspringer_table_Dparts_Bsommersparts_Csommersparts_stringclassical_W_classes_and_reps ×2passedflagtest_unitarity ×2pentagonal_serieslazy_listspermutable_typesdiagramPermutationtype, combinatoricspermutationcombinatorics · KL_polynomial_matricespermutation_actcombinatoricspermutation_conjugationcombinatoricspermutation_cyclescombinatoricspermutation_decodecombinatoricspermutation_encodecombinatoricspermutation_inversecombinatoricspermutation_iteratorcombinatoricspermutation_matrixcombinatoricspermutation_matrix_sortstablepermutation_of_root_vectorstits_centralizerpermutation_productcombinatoricspermutation_right_actcombinatoricspermutationscombinatoricspermutecombinatorics ×2 · simple_factors · character_table_reps ×3 · isomorphism_W ×4permute_characterfour · isomorphism_W ×2permute_columnscombinatoricspermute_rowscombinatoricspermuted_corootbasicpermuted_rootbasicpermuting_transporterconjugatePGLgroupsPGL_CgroupsPGL_HgroupsPGL_RgroupsPhiK_Nilpotent ×4 · field ofCyclotomicField, cyclotomicphinumber_theoryphi_datatype, number_theoryphi_data_ofnumber_theoryphi_nfield ofphi_data, number_theoryPhi_Shodge_K_type_formula ×6Phi_S_inversehodge_tensorPhi_uptoK_Nilpotent ×2pi0galoispivotfield ofPivot_info, Gaussian_elim · field ofCyclotomic_Pivot_info, cyclotomic_Gaussian_elimPivot_infotype, Gaussian_elimpivot_stepGaussian_elimpluralbasic ×2pm_simple_root_indexmisc ×2pointersbigMatricespolfield oftag_ParamPol, modulespol_formatbasic ×2polylaurentPolynomialpoly_0polynomialpoly_1polynomialpoly_2polynomialpoly_addbigMatricespoly_as_laurent_polylaurentPolynomialpoly_formatpolynomialpoly_list_addpolynomialpoly_list_subpolynomialpoly_minuspolynomialpoly_permute_basispolynomialpoly_pluspolynomialpoly_productpolynomialpoly_qpolynomialpoly_q2polynomialpoly_rows_minushodge_deformpoly_subbigMatricesposcoroot_indexbasicposcoroot_sumbasicPosettype, posetposet_inverseposetposets_equalposetpositive_imaginary_roots_and_corootsbasic ×2positive_real_roots_and_corootsbasic ×2positive_to_negativebasicposroot_as_sum_of_simplemiscposroot_Cayleysynthetic ×2posroot_crosssynthetic ×3posroot_indexbasicposroot_indicesLevi_subgroupsposroot_inv_Cayleysyntheticposroot_statussyntheticposroot_sumbasicpotential_cellcellspower_mapcharacter_tablespower_modnumber_theorypower_of_primitive_rootcyclotomicpower_setbasic ×2power_timeshodgeParamLaurentPolpre_foldedtwisted_root_datumpreimageexceptionalprependlazy_listspresent_inbasicprettyPrintmisc ×2prime_candidats_afternumber_theoryprime_divisorsnumber_theoryprime_factors_phifield ofphi_data, number_theoryprime_phi_datanumber_theoryprimesnumber_theoryprimitive_rootcyclotomicprincipal_blocknilpotent_orbitsprincipal_orbitnilpotent_orbitsprincipal_submatrixmatrixprinthodge_functionsprint_blockbasicprint_blockdbasicprint_blockubasicprint_branch_irrprint_K_types ×4print_branch_irr_longprint_K_types ×4print_branch_K_irr_longprint_K_types ×2print_branch_K_std_longprint_K_types ×2print_branch_stdprint_K_types ×5print_branch_std_longprint_K_types ×4print_by_K_normK_norm ×3print_by_K_norm_shortK_normprint_c_form_irreducible_big_longextParamPol ×2print_Cartan_infobasicprint_character_formulaklprint_classesW_classesprint_component_infonilpotent_orbits ×2print_component_info_altnilpotent_orbitsprint_component_info_longnilpotent_orbits ×2print_component_info_shortnilpotent_orbitsprint_composition_seriesklprint_conjugacy_classesW_classes ×2print_conjugacy_classes_longW_classes ×2print_conjugacy_classes_medW_classesprint_elliptic_conjugacy_classesW_classesprint_elliptic_conjugacy_classes_longW_classesprint_ext_blockextended ×3print_extended_blockbasicprint_extended_character_formulaextParamPol ×2print_extended_composition_seriesextParamPol ×2print_extended_indicesextParamPolprint_formattedklprint_graded_composition_seriesjantzen ×5print_hermitian_form_irreduciblehermitian ×4print_hermitian_form_irreducible_longhermitian ×2print_Hn_repW_reps_type_BCprint_Hn_rep_compactW_reps_type_BCprint_Hn_repsW_reps_type_BCprint_Hn_reps_compactW_reps_type_BCprint_hodge_irrhodge_K_type_formulaprint_hodge_irr_longhodge_K_type_formulaprint_hodge_K_type_mathodge_testprint_hodge_K_type_mat_trivialhodge_testprint_hodge_stdhodge_K_type_formulaprint_hodge_std_longhodge_K_type_formulaprint_inner_formsgroup_operationsprint_is_unitaryhermitianprint_is_unitary_bigextParamPolprint_K_parametersK_norm ×3print_K_parameters_by_heightK_norm ×2print_K_parameters_by_K_normK_norm ×2print_K_signature_irrprint_K_types ×2print_K_typesK_types ×2print_KGBbasicprint_KL_basisbasicprint_KL_listbasicprint_linesbasicprint_matrix_compactmatrixprint_muconvert_c_formprint_nilpotent_orbit_partitionsommersprint_nilpotent_orbit_partitionssommers ×2print_nilpotent_orbit_partitions_special_onlysommersprint_number_unipotentsfinite_unipotentsprint_prim_KLbasicprint_primitive_ideal_infoprojectors_using_character_tables ×2print_real_formsgroup_operationsprint_stablestableprint_stable_at_singularstable ×2print_stable_at_singular_unsortedstableprint_stable_sumsstable ×2print_strong_realgaloisprint_sumsstableprint_testtest_unitarity ×2print_test_all_real_induced_one_dimensionaltest_unitarityprint_test_Aqtest_unitarity ×2print_test_onetest_unitarityprint_test_spherical_unipotenttest_unitarityprint_test_Upq_Aqtest_unitarity ×2print_theta_stable_parabolicsparabolicsprint_twisted_c_form_irreducible_longhermitianprint_W_cell_graphcell_graphprint_W_cellsbasicprint_W_graphbasicprint_with_lengthklprint_wrepW_reps_type_BCprint_wrep_cptW_reps_type_BCprint_wrepsW_reps_type_BCprint_wreps_cptW_reps_type_BCprint_Zcenter ×2printable_real_nilpotentnilpotent_orbitsprintParamPolstableprintPolypolynomial ×2printPolyMatrixpolynomial ×4prints_linesbasicproductbasic ×4 · character_tablesproduct_of_cyclotomiccyclotomicproject_KK ×4project_on_centerinductionproject_on_dominant_coneK_highest_weights ×2project_on_simple_factorsimple_factors ×4 · subgroupsproject_to_dominant_conebasicprojection_to_K_matrixK ×2projectorK_Nilpotent · projectors_using_character_tables ×3projector_mod_imagelatticeprojector_newnew_conjugacyprojector_new_plusnew_conjugacyprojector_to_imagelatticeprojector_verboseprojectors_using_character_tablesprojectorsprojectors_using_character_tables ×3projectors_newnew_conjugacyprojectors_new_plusnew_conjugacyprojectors_verboseprojectors_using_character_tables ×2promotetits_centralizer ×2proper_Levi_subgroupssubgroupsproper_maximal_pseudo_Levissubgroupsproper_subgroupssubgroupsprunerestricted_rootspsG2_unitary_dualpseudo_Levinilpotent_orbitspseudo_Levi_subgroupssubgroups ×2pseudo_Levisnilpotent_orbits ×2pseudo_root_indicesnilpotent_orbitspseudo_rootsnilpotent_orbitsPsi_irrstable · translate ×3Psi_Shodge_functionsPSLgroups ×2PSL_CgroupsPSL_HgroupsPSL_RgroupsPSOgroupsPSO_stargroupsPSpgroups ×3PSp_CgroupsPSp_HgroupsPSp_RgroupsPSUgroups ×2puritybasicpushcells
Q
qsommers · L_packetQ_and_P_X_matricesfield ofKNilpotentData, K_NilpotentQ_matricesK_NilpotentQ_v_inversehodge_deformQmodZ_orderweyl_character_formulaquad_testcoherent_irreducible ×3quasicompact_formbasicquotienthodgeParamLaurentPolquotient_matrixlattice
R
RgroupsrK_type_formular_adjustbasic · tabulateR_K_domW_KR_K_dom_muW_KR_K_dom_mu_orbitW_Kradicalgroup_operations ×2radical_basisbasicradical_characterK_normrangebasicrankbasic · combinatorics ×4 · sommers · affine · character_tablesrank_KK ×2rankingsort ×6rat_as_intbasicrat_polytype, polynomialrational_inverseratmatratmattype, ratmatratmat_as_matratmatratmat_to_bigmatratmatratvec_as_vecbasicratvec_hashtype, hashratvec_to_stringratmatratvecs_as_ratmatratmatraw_KLbasicRC_simpleis_normalrdfield ofgood_data, weyltosemisimple · field ofLeviInfo, Levi_subgroups · field ofTwistedRootDatum, twisted_root_datum · field ofAffineDatum, affine · field ofDisconnectedGroup, disconnectedrd_dfield ofComplexNilpotent_d, disconnectedrd_E6exceptionalNilpotentDatard_E7exceptionalNilpotentDatard_E8exceptionalNilpotentDatard_F4exceptionalNilpotentDatard_G2exceptionalNilpotentDatareal_complex_torusbasicreal_corootsbasicreal_formbasic · field ofKNilpotentData, K_Nilpotent · weak_packets_precomputed_cell_traces · parabolics · K · nilpotent_orbits ×2 · hodgeParamLaurentPol · hodgeParamPol ×3 · field ofhodge_function, hodge_functionsreal_formsbasicreal_forms_given_central_invariantgaloisreal_forms_ofK_Nilpotentreal_induce_irreducibleinductionreal_induce_irreducible_as_sum_of_standardsinductionreal_induce_irreducible_finalinductionreal_induce_irreducible_final_verboseinductionreal_induce_irreducible_verboseinductionreal_induce_standardinduction ×2real_induced_from_one_dimaqlreal_Leviparabolicsreal_Levi_by_wtparabolicsreal_nilpotentnilpotent_orbitsreal_nilpotent_orbit_KGBsnilpotent_orbitsreal_nilpotent_orbit_KGPsnilpotent_orbitsreal_nilpotent_orbitsnilpotent_orbits ×3real_orbit_numberK_Nilpotentreal_orbitsfield ofKNilpotentData, K_Nilpotentreal_parabolicparabolicsreal_parabolic_by_wtparabolicsreal_poscorootsbasic ×2real_posrootsbasic ×2real_quaternionicfinite_dimensional_signaturereal_rootsbasicreal_roots_and_corootsbasic ×2real_sysbasic ×2real_typebasic ×2RealForm_hashtype, hashRealNilpotenttype, nilpotent_orbitsrearrangehodgeParamLaurentPol · hodgeParamPol ×2recursive_deformextParamPol · ext_deform ×2reduceextParamPol · K_highest_weights ×2reduce_good_rangeinductionreduce_modcyclotomicreduce_ratvecs_mod_latticeweyl_character_formularefine_raw_dataall_finite_orderreflectbasic ×4 · affine ×6reflect_or_affine_reflectaffinereflectionbasic ×2 · field ofWeylClassTable, W_classes · character_tablesreflection_cobasicregroupsommersregular_central_elementsubgroupsregular_central_elementssubgroupsrelative_fundamental_groupcenterremove_duplicatesrestricted_roots · parameters · nilpotent_orbits · disconnectedremove_zerosrestricted_rootsreorderW_classesreorder_diagram_Bourbakisimple_factorsrepeat_partscombinatoricsreportweyltosemisimplerepresentativeparabolicsrepresentatives_bysortreqnilpotent_inductionrequired_solutionbasic ×3requisitionbasic ×2restrict_actionlatticerestrict_charactercharacter_table_reps ×4restrict_representation_isotypicprojectors_using_character_tablesrestricted_rootsrestricted_rootsrestricted_roots_longrestricted_rootsrestricted_roots_rawrestricted_rootsrestricted_roots_shortrestricted_rootsreversebasic · coherent_irreduciblereverse_pairsweyltosemisimplereverse_sortsort ×3rhobasic · nilpotent_orbit_partitions · nilpotent_orbits · extended_miscrho2field ofStdLeviOrbit, Levi_subgroupsrho2_domfield ofrho_data, Levi_subgroupsrho_cK ×2rho_checkbasic · extended_miscrho_check_diffbasicrho_check_ibasic ×2rho_check_rbasic ×2rho_cibasicrho_coverdirac_indexrho_datatype, Levi_subgroupsrho_diffbasicrho_ibasic ×2rho_KK ×2rho_lparabolics ×2rho_Levi_by_cwtparabolicsrho_ncibasicrho_rbasic ×2rho_Sparabolics ×2 · induction ×2rho_shiftsK_Nilpotentrho_stabiliser_orbitLevi_subgroupsrho_uparabolics ×2rho_u_by_cwtparabolicsrho_u_by_wtparabolicsrho_u_cxinductionrho_u_cx_Tinductionrho_u_icinductionrightcomplex ×2 · tits ×3right_cellssub_cellsright_copysub_cellsright_corootssub_cellsright_factorssub_cellsright_inversematrix · ratmatright_reflectbasic ×2right_root_indicessub_cellsright_rootssub_cellsrising_powercombinatoricsrlex_cmp_partitionscombinatoricsrlex_leqsortrlex_leq_partitionscombinatoricsrootbasicroot_as_sum_of_simplemiscroot_datumbasic ×10 · field ofWGraph, W_reps · W_reps · K_Nilpotent · sommers ×2 · field ofComplexParabolic, parabolics · parabolics · K · field ofTits_elt, tits · field ofComplexNilpotent, nilpotent_orbits · nilpotent_orbits · W_classes · extended_misc · character_tables · springer_tables · disconnected · field ofStructureConstantTable, structure_constants · cyclotomic_Lie_algebra · bracket · exceptional ×2 · field ofNilpotentDatum, exceptional · field ofNilpotentPoset, nilpotent_posetsroot_datum_from_positivebasicroot_indicesbasicroot_lengthmiscroot_lengthsWeylgrouproot_of_unitycyclotomicroot_orbitscombinatoricsroot_partcyclotomic_Lie_algebra · bracketroot_part_arraycyclotomic_Lie_algebra · bracketroot_permutationisomorphismroot_permutationsisomorphismroot_reflectionWeylgrouproot_span_projectorbasicroot_stringmisc ×2RootDatum_hashtype, hashrootsbasic · nilpotent_orbitsroots_all_positivebasicroots_by_heightmiscroots_of_heightmiscroots_same_restrictionnilpotent_centralizerrounded_log_2GK_dimensionrowratmatrow_echelonmatrixrowsratmatrows_withbasic ×3 · ratmat ×3rqfinite_dimensional_signaturerun_hodge_testshodge_test ×2run_reportsgood_W_representatives
S
Scoherent_irreducible ×7 · field ofKGPElt, parabolics · field ofComplexParabolic, parabolicssbasic · ratmat ×2S_invcoherent_irreducible ×9S_inv_pluscoherent_irreducibles_one_nc_cx_restricted_rootsK_Nilpotents_one_rootsK_Nilpotents_one_roots_restrictedK_Nilpotents_partbasic · misc · K_typess_to_1basic ×3s_to_minus_1basic ×3S_weightnilpotent_orbitssame_ascombinatorics ×3same_complex_parabolicsadams_johnsonsame_coweight_projection_simple_factorsimple_factorssame_weight_projection_simple_factorsimple_factorssanitizediagramsaturatenilpotent_orbits ×2 · disconnected ×2 · nilpotent_posetssaturated_spanbasicsaturating_orbitsnilpotent_orbitssaturationlatticesaturation_quotient_basislatticesave_sratmatscalar_matcyclotomicMat ×2scalar_multiplypolynomialscalar_poly_matrixpolynomialscalar_productcharacter_tablesscale_bylazy_listssearchK_Nilpotent ×3 · field ofHash, hashsearch_probable_generatornumber_theory ×2search_probable_primenumber_theoryseat_belt_onbasicseed_complex_nilpotent_posetnilpotent_posetsselecttruncated_induction ×2 · field ofLeviInfo, Levi_subgroupsselect_both_degreestruncated_inductionselect_class_terms_from_ParamPolinductionselect_columnslatticeselect_degreetruncated_inductionselect_generic_degreetruncated_inductionselect_rowslatticeself_intersectcomplexsemisimplebasicsemisimple_conjugacy_class_mod_torus_repstwisted_conjugacy ×2semisimple_conjugacy_class_repstwisted_conjugacy ×2semisimple_elementnilpotent_orbit_partitions ×2semisimple_partcenter · cyclotomic_Lie_algebra · bracketsemisimple_rankbasicseparate_by_infinitesimal_characterbasicserieslazy_listsseries_0lazy_listsseries_1lazy_listsseries_precisionlazy_listsset_bit_positionsbasic ×2set_first_unset_bitbasicset_generic_degreegeck_generic ×2set_generic_degreesgeck_genericset_generic_degrees_2geck_genericset_generic_degrees_3geck_genericset_generic_degrees_geckgeck_genericset_generic_degrees_geck_longgeck_genericset_generic_degrees_plusgeck_genericsgnWeylgroup · misc ×2sgn_polypolynomialshapepolynomial · cyclotomicMatshifthodge_tensor · field ofhodgeParamLaurentPol, hodgeParamLaurentPol · hodgeParamPol ×2 · laurentPolynomial · lazy_listsshift_by_minus_1weyltosemisimpleshift_closures_by_oneexceptionalshort_formatG2_unitary_dual · extended_miscshort_stringsub_cellsshortenK_normshortensbruhatshowmodules ×4 · K_Nilpotent · good_W_representatives ×2 · arthur_parameters ×2 · sub_cells ×4 · associated_variety_annihilator · geck_generic · L_packet · ratmat · Levi_subgroups · nilpotent_orbits · subgroups ×3 · poset · cyclotomic · polynomial · character_tables · springer_tables · hodgeParamLaurentPol · hodgeParamPol ×2 · laurentPolynomial · weak_packets ×3 · cyclotomic_Lie_algebra · cyclotomicMat ×3 · bracket · exceptional ×2 · nilpotent_posets ×2 · lazy_listsshow_A_barlusztig_cells ×2show_big_tablefourshow_big_table_rfour ×2show_bruhatbruhat ×2show_bruhat_geqbruhatshow_bruhat_leqbruhatshow_bruhat_Wbruhatshow_bruhat_W_geqbruhatshow_bruhat_W_leqbruhatshow_BXYI_tablesfour ×2show_centralizer_isogeniesnilpotent_centralizershow_centralizer_isogenynilpotent_centralizershow_classescharacter_tablesshow_classes_longcharacter_tablesshow_coherent_datacoherent_characters ×6show_coherent_data_shortcoherent_charactersshow_count_orbits_and_centralizersfinite_unipotents ×2show_count_unipotentsfinite_unipotentsshow_degreesgeck_genericshow_dirac_indexdirac_index ×2show_dirac_index_param_poldirac_indexshow_longcharacter_tables · springer_tables · hodgeParamLaurentPol ×2 · hodgeParamPol ×3 · weak_packets ×4 · cyclotomic_Lie_algebra · bracket · exceptionalshow_Lusztig_cellscoherent_charactersshow_lusztig_cellslusztig_cells ×3show_lusztig_cells_classicalW_reps_type_BCshow_lusztig_cells_pluslusztig_cells ×3show_nilpotent_inductionnilpotent_inductionshow_nilpotent_orbitsshow_nilpotent_orbits ×6show_nilpotent_orbits_longshow_nilpotent_orbits ×12show_nilpotent_orbits_long_plusshow_nilpotent_orbitsshow_nilpotent_orbits_shortshow_nilpotent_orbits ×6show_nilpotent_orbits_very_longshow_nilpotent_orbits ×2show_orbits_and_repsW_reps_type_BCshow_real_nilpotent_orbitsshow_nilpotent_orbitsshow_repscharacter_tables · springer_tablesshow_richardson_orbitsnilpotent_inductionshow_shortsub_cells · weak_packets ×2show_signaturefinite_dimensional_signatureshow_springer_cells_classicalW_reps_type_BCshow_stable_sums_irrL_packetshow_subgroup_orbit_nilpotent_mapnilpotent_posetsshow_temperedweak_packetsshow_unipotent_temperedweak_packetsshow_very_longcharacter_tablesshow_weak_packets_all_formsweak_packetsshow_weak_packets_all_forms_longweak_packetsshow_Xfoursigma_lusztiglusztig_cellssigma_lusztig_longlusztig_cellssigma_lusztig_verboselusztig_cellssignbasic ×3 · tits_centralizer · coherent_irreducible · field ofWeylClassTable, W_classes · character_tables · extended ×4sign_findextendedsign_stringclassical_W_classes_and_repssign_verboseextendedsignaturefinite_dimensional_signature · character_tables ×2signature_functiontype, hodge_functionssignature_stringfinite_dimensional_signaturesignature_tracefinite_dimensional_signaturesignature_trace_stringfinite_dimensional_signaturesigned_cycle_typecombinatoricssigned_cycle_type_codecombinatoricsSigned_cyclestype, combinatoricssigned_KL_mat_at_1klsigned_multK_typessigned_permutationcombinatoricssignssommerssimple_actorW_orbitsimple_automorphismsdiagramsimple_character_tablecharacter_tables_reductivesimple_class_tableclass_tablessimple_coroot_labelsbasicsimple_factorsimple_factors ×2simple_factorssimple_factorssimple_factors_infosimple_factorssimple_imaginary_reflectionsL_packetsimple_imaginary_rootsL_packetsimple_imaginary_subsystemmiscsimple_inducenilpotent_posets · nilpotent_inductionsimple_real_subsystemmiscsimple_reflection_on_root_vectortits_centralizersimple_reflection_on_root_vectorstits_centralizer ×2simple_root_indexmisc ×2simple_root_labelsbasicsimple_root_summandmiscsimple_roots_from_coweightnilpotent_orbitssimple_roots_from_coweightsnilpotent_orbitssimple_system_from_positivebasicsimple_typelietypes ×2simplesLevi_subgroupssimplifyratmatsimply_connectedbasic ×2simply_connected_2rho_checkbasicsimply_connected_covergroup_operationssimply_connected_cover_derivedgroup_operationssimply_connected_cover_derived_infogroup_operationssimply_connected_cover_infogroup_operationssimply_connected_dual_orbitsweak_packetssinexp-generating-seriessingular_blockbasicsingular_block_ofbasicsingular_root_datumbasicsingular_simple_indicesbasicsizefield ofHash, hash · field ofEllipticDatum, exceptionalsize_of_conjugacy_classW_classessize_weak_packetcoherent_characterssize_weak_packet_intcoherent_characterssizes_of_conjugacy_classesW_classessizes_weak_packetscoherent_characters ×3SLgroups ×2SL_CgroupsSL_corootsgroupsSL_HgroupsSL_RgroupsSL_rootsgroupsslex_cmp_partitionscombinatoricsslex_leqsortslex_leq_partitionscombinatoricssliceGK_dimensionsmall_LeviW_Ksmall_Levi_coroots_KW_Ksmall_symbolW_reps_type_BCsmall_symbol_BW_reps_type_BCsmall_symbol_CW_reps_type_BCsmaller_orbitsK_Nilpotentsmallest_degreeW_reps · character_table_repssmallest_degree_summandscharacter_tablesSmith_basisbasicSn_representation_dimensioncombinatoricssndfield ofPair, basicSOgroups ×3SO_inner_classgroupsSO_real_form_numbergroupsSO_stargroups ×2solutionfield ofLinearSolution, basicsolvebasic ×3 · ratmatsolve_adbracketsolve_for_tits_elementtits_centralizersolve_for_torus_elementtits_centralizersolve_for_torus_element_oldtits_centralizersolve_ratveclatticesomefield ofMaybe, basicsortsommers · sort ×4 · nilpotent_posets · hodge_functions ×2sort_bysort ×3sort_by_dimensionnilpotent_orbits ×2 · subgroupssort_by_dimension_of_nilpotentnilpotent_posetssort_by_dual_orbitsommerssort_by_heightsort ×4 · K_normsort_by_K_normK · K_norm ×3sort_by_lengthbruhatsort_by_length_descendingbruhatsort_by_reducibilitysortsort_by_reducibility_pointssortsort_by_ss_ranksubgroupssort_K_types_by_log_2_heightGK_dimensionsort_KTypePol_by_K_normK_normsort_lexsort ×2sort_rlexsort ×2sort_slexsort ×2sort_special_firstfamiliessort_to_partitioncombinatoricssort_usort ×4 · K_types · nilpotent_posetssort_u_belowbasicsort_u_bysortsort_u_lexsort ×2sort_u_rlexsort ×2sort_u_slexsort ×2Spgroups ×3sphodge_K_type_formulaSp_CgroupsSp_HgroupsSp_Rgroupsspanning_subsettits_centralizersparsesparsesparse_columntype, sparsesparse_mattype, sparsespecialcharacter_tables · field ofNilpotentDatum, exceptionalspecial_charactercells · character_table_reps ×2special_character_inefficientcells ×2special_charactersfourspecial_closurespringer_tables ×2special_ellipticnilpotent_posetsspecial_elliptic_posetnilpotent_posetsspecial_firstW_reps_type_BCspecial_geck_dataspecial_rep ×3special_irreduciblecellsspecial_orbitsspringer_tablesspecial_orbits_indexedspringer_tablesspecial_piecespringer_tablesspecial_projectorprojectors_using_character_tables ×2special_projectorsprojectors_using_character_tables ×2special_representation_of_cellprojectors_using_character_tables ×2special_representation_starcharacter_tables · springer_tablesspecial_representationscharacter_tables · springer_tablesspecial_starspringer_tables ×2 · W_reps_type_BC ×3special_theta_stable_parabolicsaqlSpehspehSpeh_0spehspeh_0spehspeh_longspehspherical_unipotent_representationsrepresentationsSpingroupsSpin_stargroupssplitbasic ×2split_1basicsplit_and_unsplit_classesclassical_W_classes_and_repssplit_and_unsplit_repsclassical_W_classes_and_repssplit_as_intbasicsplit_classfield ofD_class, combinatorics · classical_W_classes_and_repssplit_coradical_basiscentersplit_dataGaussian_elim · cyclotomic_Gaussian_elimsplit_factor_formatbasicsplit_formbasic ×2 · group_operationssplit_formatbasicsplit_irrfield ofD_irrep, combinatoricssplit_irrepclassical_W_classes_and_repssplit_linesbasicsplit_minus_1basicsplit_radical_basiscentersplit_rankbasic ×2split_torusbasicspringerfield ofSpringerTable, springer_tablesspringer_Bspringer_table_BCspringer_by_name_E8springer_table_E8springer_by_name_table_E8springer_table_E8springer_by_signature_E7springer_table_E7springer_by_signature_lookup_E7springer_table_E7springer_Cspringer_table_BCspringer_cell_classicalW_reps_type_BC ×2springer_cells_classicalW_reps_type_BCspringer_characterspringer_tablesspringer_Dspringer_table_D ×2springer_E7springer_table_E7springer_E8springer_table_E8 ×2springer_inversespringer_tables ×2springer_inverse_specialspringer_tables ×2Springer_tablespringer_tables_reductivespringer_table_Aspringer_table_Aspringer_table_Bspringer_table_BCspringer_table_Cspringer_table_BCspringer_table_Dspringer_table_Dspringer_table_E6springer_table_E6 ×2springer_table_E7springer_table_E7 ×3springer_table_E8springer_table_E8 ×3springer_table_Fspringer_table_F ×2springer_table_Gspringer_table_G ×2Springer_table_generic_degreesgeck_genericspringer_table_simplespringer_tables_reductiveSpringerTabletype, springer_tablessquaresynthetic · parameters ×3square2parameterssquare_classesgaloissquare_is_centralsynthetic · parameters · extended_miscsquare_normalizedparameterssquare_unnormalizedparametersss_rankmisc · affinestabiliser_quotientW_orbit ×8stabilizer_elementarysubgroupsstabilizer_of_xnilpotent_orbitsstablestablestable_at_regularstablestable_at_singularstable ×3stable_at_singular_unsortedstablestable_sumsstablestable_sums_irrL_packetstable_sums_irr_in_basis_of_standardsL_packetstable_sums_irr_in_basis_of_standards_as_matricesL_packetstable_sums_irr_matL_packetstable_sums_partialstablestable_sums_stdL_packetstable_sums_std_matricesL_packetstable_test_Aq_packetstable ×2standard_datum_E6class_tablesstandard_datum_E7class_tablesstandard_datum_E8class_tablesstandard_Leviconjugatestandard_Levi_and_witnessconjugatestandard_Levi_conjugacy_representativesLevi_subgroupsstandard_Levi_coweightparabolicsstandard_Levi_lookupLevi_subgroupsstandard_Levi_weightparabolicsstandard_Levi_witnessconjugatestandard_Levischaracter_table_repsstandardizegood_W_representatives · induction ×2standardize_Lie_typelietypesstarsommers · Vogan-dualstarting_complex_nilpotent_posetnilpotent_posetsstarting_set_of_K_typeshodge_K_type_formulastatusbasic ×3 · modulesstatus_textbasic ×4status_textsbasic ×2stdmodulesstd_Levifield ofStdLeviImage, Levi_subgroupsStdLeviEltImagetype, W_classesStdLeviFindertype, Levi_subgroupsStdLeviImagetype, Levi_subgroupsStdLeviOrbittype, Levi_subgroupsStdLeviReducertype, W_classesStdLeviTabletype, Levi_subgroupsSteinberg_charactercharacter_table_repsstepGaussian_elim · cyclotomic_Gaussian_elimstrbasicstratified_diagramnilpotent_orbits ×2stratifysimple_factorsstrict_partitionscombinatoricsstrict_pseudo_Levi_subgroupssubgroupsStringnilpotent_orbit_partitionsstring_compactmatrixstring_to_diagramspringer_table_E8stringifyK_Nilpotentstrippolynomialstrip_to_partitioncombinatoricsstrip_trailing_spacestabulatestrong_componentssub_cells ×2strong_real_formsgaloisstrong_real_forms_central_invariant_egaloisstrong_real_forms_given_central_invariantgaloisstrong_real_forms_indicesgaloisstrong_real_forms_nilpotent_orbit_correct_central_invariantshow_nilpotent_orbitsstrong_real_forms_nilpotent_orbit_eshow_nilpotent_orbitsstrong_real_forms_same_typegalois ×2strong_real_forms_typegaloisstrong_testhermitianstructure_constant_tablestructure_constantsStructureConstantTabletype, structure_constantsSUgroups ×3subhodgeParamLaurentPolsub_cellssub_cellssub_datumbasic ×2sub_digraphsub_cellssub_graphsub_cells · subgroups ×2sub_graph_max_pseudo_levis_onlysubgroupssub_tablestructure_constants ×2 · exceptional ×2sub_table_distinguishedexceptionalsub_table_evenexceptionalsubgroupsubgroups ×2subgroup_by_simplesubgroupssubgroup_from_positivesubgroups ×2subgroupssubgroupssubgroups_posetsubgroups ×2subgroups_rawsubgroupssubgroups_weaksubgroupssubmergenilpotent_posetssubPosetposetsubregular_orbit_simplenilpotent_orbitssubregular_orbitsnilpotent_orbitssubsets_of_s_one_nc_cx_restricted_rootsK_Nilpotentsubspace_injection_matrixstablesubstitutelazy_listssubtract_onesommerssucceedfield ofOne_of, basicsucceedsbasicsumbasic ×10 · sommers ×2 · character_tables ×2 · cyclotomic_Lie_algebra · lazy_listssums_nci_nilrad_roots_restricted_to_H_thetanci_nilrad_rootssums_nci_nilrad_roots_wedge_k_restricted_to_H_thetanci_nilrad_rootssums_of_size_knci_nilrad_rootssupportparabolics · nilpotent_orbits · W_reps_type_BC · cyclotomic_Lie_algebra · bracketsupport_altparabolicssupport_dualparabolics · nilpotent_orbits · Vogan-dual ×2support_dual_intVogan-dualsurvivesbasicswapgenericsswapargsgenericsswapped_factorssub_cellssym_powerW_classes · character_tablessym_power_reflfield ofWeylClassTable, W_classes · character_tablesSymboltype, combinatoricssymbolcombinatorics · W_reps_type_BCsymbol_BW_reps_type_BCsymbol_CW_reps_type_BCsymbol_ranksW_reps_type_BCsymbol_to_bipartitioncombinatoricssymbolsW_reps_type_BCsymbols_equalW_reps_type_BC
T
Tcoherent_irreducible ×5tfield ofExtParam, extended_misc · field ofCFLieAlgebraElement, cyclotomic_Lie_algebra · field ofLieAlgebraElement, bracketT_invcoherent_irreducible ×2T_irrtranslate ×2T_irr_dominanthodgeParamLaurentPolT_irr_nonzerotranslateT_matricesfield ofKNilpotentData, K_NilpotentT_matrixK_NilpotentT_paramtranslate ×2T_stdtranslate ×3tableall_finite_order ×2 · field ofCharacterTable, character_tables · field ofStructureConstantTable, structure_constantstable_reducedall_finite_ordertabulatetabulate ×2tabulate_at_1kltabulate_indicesbigMatricestagfield oftag_Param, modules · field oftag_ParamPol, modulestag_Paramtype, modulestag_ParamPoltype, modulestakebasictanexp-generating-seriestangent_basisfield ofAffineSubspace, basictangent_spacefield ofaffine_subspace, Gaussian_elimtaubasic · modules · field ofWNode, W_reps · sub_cells · field ofExtParam, extended_misc · hodge_normalizetau_bitsetbasictau_complementbasic · modulestau_containingnilpotent_orbitstau_invariantsnilpotent_orbitstau_invariants_of_cellnilpotent_orbitstau_invariants_of_cell_rawnilpotent_orbitstau_qK_types_plustensorfield ofWeylClassTable, W_classes · character_tables ×2tensor_powerfield ofWeylClassTable, W_classes · character_tables ×2tensor_productfinite_dimensional · character_tables · tensor_product ×2tensor_product_u_cap_stensor_producttensor_product_wedge_k_u_cap_stensor_product ×2tensor_product_weightsfinite_dimensionaltensor_signcharacter_tablestensor_sign_indexcharacter_tablestensor_with_fdtensor_producttesttest_unitarity ×3 · all_finite_order · nilpotent_centralizer · sommers ×2 · tensor_product ×3 · nilpotent_posetstest1Vogan-dualtest2Vogan-dualtest_allspringer_tables_reductive ×2test_all_orbitsK_Nilpotent ×2test_all_real_induced_one_dimensionaltest_unitaritytest_Aqtest_unitarity ×2test_av_maximal_idealassociated_variety_annihilator ×2test_braidtest_braid ×2test_conjectureweak_packetstest_conjecture_reportweak_packets ×3test_dspringer_tables_reductive ×2test_dispringer_tables_reductivetest_dual_mapspringer_tables_reductivetest_dual_map_ispringer_tables_reductivetest_dualitydualtest_elementary_hodge_grading_irr_at_1hodge_testtest_elementary_hodge_grading_irr_at_shodge_testtest_elementary_hodge_grading_std_at_1hodge_testtest_elementary_hodge_grading_std_at_shodge_testtest_enumerated_classnew_conjugacytest_Fermatnumber_theorytest_geck_generic_degreesgeck_generictest_generic_degreesgeck_generic ×2test_hodge_grading_std_at_1hodge_testtest_hodge_grading_std_at_shodge_testtest_hodge_K_type_mathodge_K_type_formula ×2 · hodge_test ×2test_induce_orbitstruncated_inductiontest_inv_conjfourtest_K_typesK_highest_weightstest_K_types_plusK_types_plus ×2test_lG2_unitary_dualtest_linehermitiantest_longtensor_producttest_minimal_orbitsK_Nilpotent ×2test_onetest_unitaritytest_one_unitarytest_unitaritytest_parabolicsK_types_plustest_positivehodge_testtest_positive_hodge_K_type_mathodge_test ×2test_projectornew_conjugacytest_real_orbitnilpotent_orbitstest_sG2_unitary_dualtest_simple_BCW_reps_type_BCtest_simple_typebasictest_size_of_conjugacy_classesW_classes ×2test_special_geckspecial_reptest_special_mapsspecial_rep ×3test_spherical_unipotenttest_unitaritytest_springerspringer_tables_reductivetest_valid_onlysommerstest_weak_packetsweak_packetstext_saveexceptionalthetafield ofTits_elt, tits · field ofx_rep, extended_misc · field ofExtParam, extended_misctheta_induce_irreducibleinductiontheta_induce_irreducible_as_sum_of_standardsinductiontheta_induce_irreducible_coherentinductiontheta_induce_irreducible_finalinductiontheta_induce_irreducible_wgraphcoherent_irreducible ×2theta_induce_parampolinductiontheta_induce_standardinductiontheta_induce_standard_warningK_type_formulatheta_induced_unipotentsweak_packetstheta_induced_unipotents_longweak_packetstheta_orbit_repsK_Nilpotenttheta_plus_1_lambdabasic ×2theta_stable_datainductiontheta_stable_Leviparabolicstheta_stable_Levi_by_wtparabolicstheta_stable_parabolicparabolicstheta_stable_parabolic_by_wtparabolicstheta_stable_parabolicsparabolics ×2theta_stable_parabolics_maxinductiontheta_stable_parabolics_of_typeparabolicstheta_stable_parabolics_withinduction ×2theta_stable_quasi_datainductionthunkfield ofinfinite_node, lazy_liststi_verbosetruncated_inductiontimebasictimed_outfield ofmaybe_KTP, hermitiantimesGaussian_elim ×2times_sbasictitsparameterstits_actiontits_centralizer ×2tits_centralizer_weaktits_centralizer ×11tits_centralizes_weaktits_centralizer ×3tits_deltatits ×2Tits_elttype, titstits_identitytitstits_subgrouptits_centralizerto_basebasic · tits_centralizerto_base_fixed_lengthbasicto_base_polybasicto_binarymiscto_canonicallietypesto_cyclescombinatoricsto_D_classcombinatoricsto_denominatorcyclotomicto_int_polypolynomialto_integercyclotomicto_listbasicto_no_CminusWeylgroup ×2 · Kto_no_CplusWeylgroup ×2to_partition_paircombinatoricsto_rat_polypolynomialto_rationalcyclotomic · cyclotomicMatto_ratmatratmatto_rowrowratratmatto_specialspecial_repto_special_E6character_table_E6to_special_E7character_table_E7to_special_E8character_table_E8to_special_F4character_table_Fto_special_G2character_table_Gto_special_geckspecial_rep ×3to_special_geck_longspecial_rep ×3to_strmodules ×4to_str_irrmodulesto_str_K_typesmodulesto_str_stdmodulesto_stringscyclotomic_Lie_algebrato_vecshashto_walltranslatetop_left_square_blockmatrix · polynomialtorusbasic · nilpotent_centralizertorus_actiontits_centralizertorus_datumbasictorus_elementweyltosemisimple ×2torus_factorfield ofKGBElt_gen, synthetic · extendedtorus_factor_xweyl_character_formulatorus_partfield ofTits_elt, titstracebasic · weyl_character_formula ×5trace_coherentcoherent_characters ×4trace_coherent_rcoherent_characters ×2trace_longweyl_character_formula ×3trace_reportfinite_dimensional_signature · weyl_character_formula ×3trace_semisimple_simply_connectedweyl_character_formulatrace_strong_realweyl_character_formula ×2trans_closeposettransitive_containmentsubgroupstransitive_fillposettransitive_fill_oneposettranslate_debugtranslatetranslate_param_bytranslate ×2translate_to_dominantWeylgroup · extended_misctransporterconjugatetransposebasic · combinatoricstrifinite_unipotentstriv_hash_infohashtrivialbasic · field ofWeylClassTable, W_classes · character_tablestrivial_blockrepresentationstrivial_character_tablecharacter_tablestrivial_class_tableW_classestrivial_datumgroupstrivial_groupgroupstrivial_WW_repstruncateGK_dimension · truncated_induction ×2truncate_by_degree_induce_charactertruncated_inductiontruncate_degree_induce_charactertruncated_inductiontruncate_induce_charactertruncated_induction ×5truncate_induce_signcharacter_table_repstruncate_induce_trivialcharacter_table_repstTcoherent_irreducible ×5twistbasic · nilpotent_orbits · extended_misc ×2twist_by_minus_2rho_u_cap_sK_Nilpotent ×2 · inductiontwist_orbitshermitiantwisted_c_form_irreduciblehermitian ×2twisted_c_form_irreducible_as_sum_of_standardshermitiantwisted_c_form_irreducible_contributionshermitiantwisted_c_form_irreducible_longhermitiantwisted_c_form_irreducible_unnormalizedhermitiantwisted_c_form_stdhermitiantwisted_full_deformext_deformtwisted_involutionscoherent_characterstwisted_recursive_deformext_deformTwistedRootDatumtype, twisted_root_datumtwo_eigenspacebracket ×2two_rhobasic ×2two_rho_checkbasic ×2two_rho_of_pseudo_Levinilpotent_orbitstwo_rho_Sinduction ×4two_rho_uinductiontwo_rho_u_cap_kinductiontwo_rho_u_cap_sinductiontworhonilpotent_orbit_partitionstworho_cK ×2tworho_KK_highest_weightstype_B_rootsgroupstype_C_rootsgroupstype_centercentertype_D_rootsgroupstype_numbernilpotent_orbit_partitions ×2
U
Ugroupsuinductionu_cap_s_rho_shifts_and_cardinalitiesK_type_formulau_cap_s_rootsK_type_formulauflagtest_unitarity ×2un_datumLevi_subgroupsuncurrygenericsunderlying_orbitsommersungroupsommersunionhodge_K_type_formula ×2 · weyltosemisimpleunipotent_representationsweak_packets ×2unipotent_representations_by_orbitweak_packetsunipotentsweak_packets ×2uniqueW_reps · hodge_K_type_formula ×2unnormalized_torus_factorsynthetic · parametersunsafe_dividepolynomialunset_bit_positionsbasic ×2unset_first_set_bitbasicunsorted_cycle_type_GLclass_tablesunsparsesparseunsplit_classfield ofD_class, combinatorics · classical_W_classes_and_repsunsplit_irrfield ofD_irrep, combinatoricsunsplit_irrepclassical_W_classes_and_repsuntabled_testerW_classesunzipbasicup_left_cornercomplexup_right_cornercomplexupdatestructure_constantsupdate_generic_degreesgeck_generic ×5update_generic_degrees_geckgeck_generic ×2update_generic_degrees_geck_longgeck_generic ×2update_generic_degrees_using_signgeck_generic ×2update_matrix_rowpolynomialupdate_one_table_geckgeck_genericupdate_one_table_mixed_strategygeck_genericupdate_pairsK_Nilpotentupdate_Q_and_P_X_matricesK_Nilpotentupdate_rowpolynomialupdate_structure_constant_tablestructure_constantsupdate_T_matricesK_Nilpotentupdate_Y_matricesK_Nilpotentupperbasic ×2upper_unitriangular_inversematrix · polynomialuprootLevi_subgroups
V
vfield ofKNilpotentData, K_Nilpotent · field ofCyclotomicFieldElement, cyclotomic · field ofx_rep, extended_miscv_inverselaurentPolynomialv_laurentlaurentPolynomialv_laurent_powerlaurentPolynomialv_laurent_squaredlaurentPolynomialv_minus_powerlaurentPolynomialv_minus_twolaurentPolynomialv_powerpolynomialv_sumlaurentPolynomialv_to_1hodgeParamLaurentPol · hodgeParamPol ×2v_to_shodgeParamPol ×2v_to_the_k_times_Q_v_inversehodge_deformvalidextended_miscvalid_signssommersvalid_symbolssommersvalidatesommers ×2validate_signssommersvanishingstablevariants_Bsommers ×2variants_Csommers ×2vec_hashtype, hashvec_posetW_ordervec_solvelatticevecsfield ofEigenPair, good_W_representatives · W_orderVectorK_Nilpotent ×2vectorbasic · K_Nilpotent ×2veepolynomialverbose_fdsigfinite_dimensional_signatureverbose_traceweyl_character_formulavertex_and_W_cellcellsvertex_and_W_cellsW_repsvery_simple_factorssimple_factorsviable_Levisnilpotent_orbitsview_charcharacter_tables ×2view_complexcomplexview_multiplicitiescharacter_tablesvshowpolynomial
W
WW_orbitwcomplex · Weylgroup ×2 · field oforbit_entry, Levi_subgroups · field ofother_entry, Levi_subgroups · field ofAffineWeylElt, affine · field ofi_laurent_poly, laurentPolynomial · field ofEllipticDatum, exceptionalw0basicW_c_perpW_KW_cellcellsW_cell_graphcell_graphW_cell_graph_datacell_graphW_cell_graph_dotcell_graphW_cell_ofcells ×2W_cell_ordercell_graphW_cells_ofW_repsW_class_tableW_classes ×2W_class_table_genericW_classesW_class_table_untabledW_classesW_crossbasicW_eltbasicW_elt_of_reflectionbasic ×2W_genbasicW_gensbasicW_graphW_orderW_graph_ofcoherent_irreducibleW_iteratorW_orbitW_KW_KW_mod_W_LK_normW_orbitW_orbit ×8W_orbit_torus_elementweyl_character_formulaW_orbit_with_witnessW_orbit ×8W_parabolic_iteratorW_orbitW_parabolic_iterator_with_actionW_orbitw_parametercomplexw_parameter1complexW_posetW_orderW_reptype, W_repswall_projectorbasicWCelltype, W_repsweak_left_inversematrixweak_packetweak_packets_precomputed_cell_traces · weak_packets ×2weak_packet_intweak_packets_precomputed_cell_traces ×2 · weak_packets ×2weak_packet_reportweak_packetsweak_packet_report_indweak_packetsweak_packetsweak_packets_precomputed_cell_traces ×5 · weak_packets ×4weak_packets_all_formsweak_packetsweak_packets_evenweak_packetsweak_packets_preweak_packets_precomputed_cell_tracesweak_testhermitianweakly_maximal_pseudo_Levis_simplesubgroupsweyl_denominator_quotientweyl_character_formulaWeyl_dimfinite_dimensionalWeylClassTabletype, W_classeswf_aqs_paramaql ×2wf_aqs_param_polaql ×2wf_one_dim_paramsaqlWGraphtype, W_repswherebasicwidthbasicwith_decimalsbasicWNodetype, W_repswrepW_reps_type_BC ×3wrepsW_reps_type_BC ×2wt_multtensor_productwts_of_fdfinite_dimensional
X
Xfield ofCFLieAlgebraElement, cyclotomic_Lie_algebra · cyclotomic_Lie_algebra ×2 · field ofLieAlgebraElement, bracket · bracket ×2 · lazy_listsxbasic ×2 · field ofKGPElt, parabolics · field ofKHighestWeight, K · field ofKGBratvec, hash · field ofRealNilpotent, nilpotent_orbits · extended_miscX_alphacyclotomic_Lie_algebra ×2 · bracket ×2x_lG2_unitary_dualx_minparabolicsx_openbasicx_reptype, extended_miscx_sG2_unitary_dualxlambda_hashtype, hashXORbasic
Y
yextended_miscy_genL_packetY_matricesfield ofKNilpotentData, K_Nilpotent
Z
zextendedZ_2centerZ_hatcenter ×2z_quotextendedzerocyclotomiczero_corootsgood_W_representativeszero_laurent_polylaurentPolynomialzero_orbitnilpotent_orbitszero_poly_matrixpolynomial ×2zero_poly_rowpolynomialzero_rootsall_finite_orderzero_simple_corootsparabolicszero_simple_rootsparabolicszeta_powercyclotomiczipbasic
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