atlas Library
Script Files
The 175 script files that are read when you load <all.at, with their
5643 definitions. Descriptions are the first line of each file’s own header comment;
see also the alphabetical index of defined names.
Files loaded by all.at 175 files, alphabetical
| File | Definitions | From the file’s header comment |
|---|---|---|
adams_johnson.at | 20 | |
affine.at | 62 | <outer.at |
all_finite_order.at | 31 | The labels m_i on the Dynkin diagram representing the coefficient of the simple roots in the highest root. … |
aql.at | 24 | |
arthur_parameters.at | 6 | parametrizing sets of unipotent Arthur parameters: see notesOnUnipotentParamters.pdf in Dropbox … |
associated_variety_annihilator.at | 37 | |
basic.at | 820 | |
bigMatrices.at | 20 | The purpose of this file is to do extended group computations working with … |
bracket.at | 58 | Lie bracket |
bruhat.at | 24 | bruhat order: given x,y\in KGB(G) compute x<=y (boolean) … |
c_form_branch.at | 5 | |
cell_graph.at | 7 | Graph on W-cells of the block of p, numbered as in block_of(p) and W_cells(p). … |
cells.at | 30 | |
center.at | 31 | center Z and dual Z_hat of complex group or real form … |
certificate.at | 2 | |
character_table_E6.at | 7 | |
character_table_E7.at | 9 | |
character_table_E8.at | 6 | |
character_table_F.at | 8 | the function |classes_Kondo_F4| defined in class_tables.at lists conjugacy class representatives for any $F_4T_k$ type root datum in a fixed order, which order is used below to write down characters. … |
character_table_G.at | 4 | the list |G2_class_words| of conjugacy class representatives is fixed in … |
character_table_reps.at | 36 | |
character_tables.at | 72 | |
character_tables_reductive.at | 4 | |
class_tables.at | 50 | The purpose of this module is to group case-by-case definitions of W-class tables for root data with a specified simple Cartan matrix type, and give a definion of |class_table@RootDatum|. … |
classical_character_tables.at | 15 | type A |
classical_W_classes_and_reps.at | 15 | conjugacy classes and representations of classical Weyl groups … |
coherent.at | 15 | computing coherent continuations |
coherent_characters.at | 62 | character of coherent representation on parameters, KGB, and involutions |
coherent_irreducible.at | 89 | |
combinatorics.at | 129 | The purpose of this module is to collect basic combinatorial functions, … |
complex.at | 40 | |
conjugate.at | 14 | Goal: given two sub-root systems of |rd| associated to pseudo Levi subgroups, … |
convert_c_form.at | 11 | commands for converting from c-form to hermitian-form … |
coordinates.at | 12 | |
cross_W_orbit.at | 4 | |
cyclotomic.at | 52 | This file implements arithmetic in cyclotomic fields … |
cyclotomic_field_bracket.at | 0 | moved to cyclotomic_Lie_algebra.at |
cyclotomic_Gaussian_elim.at | 17 | Gaussian elimination over cyclotomic fields … |
cyclotomic_Lie_algebra.at | 47 | Lie algebra over cyclotomic field |
cyclotomicMat.at | 46 | |
diagram.at | 5 | Functionality related to Lie types, Dynkin diagrams, and their automorphisms |
dirac_index.at | 13 | Dirac index for equal rank groups … |
disconnected.at | 13 | data type for certain disconnected complex reductive groups … |
dual.at | 5 | some similar stuff to Vogan-dual.at, also some extra functionality |
E6_sc_q_unipdata.at | 1 | |
E6_sc_s_unipdata.at | 1 | |
E7_sc_h_unipdata.at | 1 | |
E7_sc_q_unipdata.at | 1 | |
E7_sc_s_unipdata.at | 1 | |
e8_gap.at | 7 | gap character table for E8, processed to be input into atlas … |
E8_q_unipdata.at | 1 | |
E8_s_unipdata.at | 1 | List of all unipotent representations of E8_s, from Steve's computations. |
elliptic.at | 14 | The purpose of this file is listing conjugacy classes of elliptic elements of … |
exceptional.at | 35 | Tables of Weyl group conjugacy classes and Nilpotent Orbits … |
exceptionalNilpotentData.at | 17 | nilpotent orbit data for exceptional simple groups … |
exp-generating-series.at | 13 | some help with exponential generating series, which are lazily computed … |
ext_deform.at | 7 | |
extended.at | 42 | references: … |
extended_misc.at | 42 | |
extended_types.at | 8 | types of extended parameters: … |
extParamPol.at | 38 | implement ParamPol for extended parameters |
F4_s_unipdata.at | 1 | |
families.at | 4 | |
finite_dimensional.at | 17 | finite dimensional representations of G(C) |
finite_dimensional_signature.at | 24 | some functions related to Frobenius-Schur indicator, … |
finite_unipotents.at | 15 | |
four.at | 19 | |
G2_unitary_dual.at | 25 | |
galois.at | 25 | G is a RealForm … |
Gaussian_elim.at | 16 | Gaussian elimination on matrices represented by values of type [[rat]] … |
geck_generic.at | 48 | |
generate_groups.at | 6 | |
generic_degrees.at | 2 | |
generics.at | 11 | |
GK_dimension.at | 8 | |
good_W_representatives.at | 22 | good conjugacy class representatives in W, … |
group_operations.at | 26 | |
groups.at | 97 | |
hash.at | 47 | Hash tables for any type |T| that can provide hahshing and equality testing. … |
hermitian.at | 44 | |
hodge_deform.at | 18 | |
hodge_functions.at | 21 | basics of functions from K-hat to Z,W and Z[v] |
hodge_K_type_formula.at | 45 | |
hodge_normalize.at | 11 | |
hodge_tensor.at | 20 | see hodgeTempered.pdf in Dropbox … |
hodge_test.at | 19 | |
hodgeParamLaurentPol.at | 39 | see hodgeParamPol.at and hodgeParamLaurentPol.pdf … |
hodgeParamPol.at | 52 | |
induction.at | 103 | ! Parabolic induction from real and $\theta$-stable parabolics; cuspidal and $\theta$-stable data of a parameter, and some functions related to $\theta$-stable parabolics. … |
is_normal.at | 7 | Two different definitions of normal: … |
isomorphism.at | 7 | permutations relating Cartan matrices … |
isomorphism_W.at | 14 | some isomorphisms of Weyl groups not necessarily coming from root systems … |
jantzen.at | 12 | I=standard, J'=irreducible Q(J',I)=\sum a_i q^i a_{(l(I)-l(J')-n)/2}=mult of J' in level n F_n of Jantzen filtration where I=I_0\supset I_1\supset ... … |
K.at | 45 | ! Embedding of the complex group K defined by compact imaginary root system … |
K_highest_weights.at | 68 | |
K_Nilpotent.at | 97 | |
K_norm.at | 52 | |
K_type_formula.at | 9 | |
K_types.at | 17 | |
K_types_plus.at | 12 | |
kl.at | 15 | KL stuff, including character formulas and composition series … |
KL_polynomial_matrices.at | 24 | |
L_packet.at | 37 | |
lattice.at | 31 | General linear algebra over $\Z$. … |
laurentPolynomial.at | 36 | laurent polynomial in indeterminate v with integer coefficients … |
lazy_lists.at | 48 | This file demonstrates how axis can handle lazy infinite lists (of any type) |
Levi_subgroups.at | 37 | This file groups function concerning classification of and computation with Levi subgroups. … |
lietypes.at | 43 | |
lusztig_cells.at | 21 | the Lusztig map goes from triples (O,x,xi) to W^ … |
matrix.at | 19 | Functions for some non elementary but general matrix operations, like finding a left or right inverse of a given matrix, if one exists. |
misc.at | 54 | |
modules.at | 46 | |
nci_nilrad_roots.at | 7 | |
new_conjugacy.at | 17 | |
nilpotent_centralizer.at | 19 | computing the centralizer of a complex nilpotent … |
nilpotent_induction.at | 7 | |
nilpotent_orbit_partitions.at | 17 | (complex) nilpotent orbits for simple classical groups, … |
nilpotent_orbits.at | 168 | |
nilpotent_orbits_exceptional.at | 7 | lists of 1/2 h(O^\vee) for exceptional groups … |
nilpotent_posets.at | 30 | closure relations for nilpotent orbits |
number_theory.at | 24 | |
parabolics.at | 100 | See "Parabolic Subgroups and Induction" on the Atlas web site. … |
parameters.at | 32 | various ways of defining parameters |
polynomial.at | 129 | Several representations of univariate polynomials are defined below, all have … |
poset.at | 21 | Partially ordered sets |
print_K_types.at | 23 | this file used to be called K_types.at … |
projectors_using_character_tables.at | 23 | |
ratmat.at | 70 | implement type |ratmat| that makes doing linear algebra over $\Q$ possible … |
representations.at | 16 | <nilpotent.at |
restricted_roots.at | 12 | compute the root system of A in G where … |
show_nilpotent_orbits.at | 35 | |
simple_factors.at | 17 | <Weylgroup.at {for invariant_form} |
sommers.at | 76 | |
sort.at | 56 | |
sparse.at | 6 | multiplication of a square integer matrix times … |
special_rep.at | 18 | |
speh.at | 4 | |
springer_table_A.at | 5 | Springer correspondence from nilpotent orbits to representations of W in type A … |
springer_table_BC.at | 29 | |
springer_table_D.at | 12 | Springer correspondence from nilpotent orbits to representations of W, type D |
springer_table_E6.at | 4 | Let are 21 nilpotent orbits for E6: … |
springer_table_E7.at | 9 | atlas> show_nilpotent_orbits("E7".simply_connected) … |
springer_table_E8.at | 24 | name,diagram,dim,special,dual,A/Abar |
springer_table_F.at | 4 | Like for G2, the Springer table maps are given in tabular form, where nilpotent orbits are analysed through their diagram. … |
springer_table_G.at | 2 | for |rd="G2".simply_connected|, the command |orbits(rd)| returns 5 orbits, whose diagrams are, in order, [0,0],[0,1],[1,0],[0,2],[2,2]. … |
springer_tables.at | 32 | tables encoding the Springer correspondence |
springer_tables_reductive.at | 11 | |
stable.at | 57 | stable virtual characters … |
structure_constants.at | 21 | structure constants for the Lie algebra … |
sub_cells.at | 36 | Suppose G is a RootDatum, and \theta is a algebraic involution of G … |
subgroups.at | 80 | The functions deal with constructing Levi systems cut out by various linear conditions (being orthogonal to a given set of coroots), and their root data. … |
synthetic.at | 25 | |
tabulate.at | 7 | |
tensor_product.at | 28 | |
test_braid.at | 3 | |
test_unitarity.at | 23 | test list [(Param p,bool answer)], … |
tits.at | 22 | An element of the (\delta-extended) Tits group is represented by (RootDatum … |
tits_centralizer.at | 53 | |
translate.at | 18 | |
truncated_induction.at | 25 | if L is a Levi subgroup of G, and pi an irreducible representation of W_L, … |
twisted_conjugacy.at | 10 | twisted semisimple conjugacy classes (including trivial case of trivial twist) … |
twisted_root_datum.at | 16 | |
unitary.at | 3 | |
Vogan-dual.at | 24 | A first main objective of this script is to define a function |dual_KGB| that associates to a |Param| value a KGB element for a computed dual real form. … |
W_classes.at | 63 | This file serves to compute with Weyl group conjugacy classes and characters. … |
W_K.at | 17 | full Weyl group W_K of disconnected maximal compact subgroup … |
W_orbit.at | 39 | |
W_order.at | 6 | order on conjugacy classes of W … |
W_reps.at | 27 | |
W_reps_type_BC.at | 83 | types C and B … |
weak_packets.at | 59 | computing weak unipotent Arthur packets |
weak_packets_precomputed_cell_traces.at | 12 | computing weak packets using precomputed cell_traces mainly used for E8_s … |
weyl_character_formula.at | 23 | ! Weyl character formula computed at elements of finite order … |
Weylgroup.at | 46 | Functions for computing with Weyl group elements |
weyltosemisimple.at | 8 |
Generated from atlas-scripts at commit 648506c (2026-10-13).