aql.at Function References¶
inf_chars_dom_for_L¶
inf_chars_dom_for_L:Param p, Parabolic P->[ratvec] Defined in line number 9.Given a parameter p for G and a real parabolic P, list all Weyl(G) conjugates of the infinitesimal character of p that are dominant for L.
inf_chars_for_L¶
inf_chars_for_L:Param p,Parabolic P->[ratvec] Defined in line number 18.Given a parameter p for G and a theta-stable parabolic P, list all infinitesimal characters v for L so that v+rho(u) is the infinitesimal character of p.
inf_chars_for_L¶
inf_chars_for_L:ratvec gamma,Parabolic P->[ratvec] Defined in line number 28.Given an infinitesimal character gamma for G and a theta-stable parabolic P, list all infinitesimal characters v for L so that v+rho(u) is the infinitesimal character of p.
one_dim_params_gamma¶
one_dim_params_gamma:ratvec ic, Parabolic P->[Param] Defined in line number 38.List all one-dimensional unitary characters with given infinitesimal character.
wf_one_dim_params¶
wf_one_dim_params:ratvec ic, Parabolic P->[Param] Defined in line number 48.List all one-dimensional unitary characters, in the weakly fair range, of L, with given infinitesimal character.
wf_aqs_param_pol¶
wf_aqs_param_pol:Param p, Parabolic P->[(Param,ParamPol)] Defined in line number 55.Auxiliary function: List of all unitary weakly fair Aq(lambda) modules with infinitesimal character of p, and induced from P.
wf_aqs_param¶
wf_aqs_param:Param p, Parabolic P->[(Param,Param)] Defined in line number 67.Auxiliary function: As previous function, except a list of all parameters occurring as constitutents of such modules.
is_weakly_fair_Aq_from_P¶
is_weakly_fair_Aq_from_P:Param p, Parabolic P->bool Defined in line number 77.Decide whether p is the parameter of a (constituent of a) unitary weakly fair Aq(lambda) induced from parabolic P.
special_theta_stable_parabolics¶
special_theta_stable_parabolics:RealForm G->[Parabolic] Defined in line number 82.List all proper theta-stable parabolics for G that are not Borels.
all_wf_Aq_with_ic_of¶
all_wf_Aq_with_ic_of:Param p->[Param] Defined in line number 90.List all parameters of constituents of weakly fair Aq(lambda) modules with the same infinitesimal character as p.
is_weakly_fair_Aq¶
is_weakly_fair_Aq:Param p->bool Defined in line number 98.Determine whether parameter p is that of a (constituent of a) unitary weakly fair Aq(lambda) module.
is_wf_induced_from_one_dim¶
is_wf_induced_from_one_dim:Param p->[(Parabolic,Param)] Defined in line number 114.List all one-dimensional unitary parameters pL so that p is theta-induced from pL in the weakly fair range.
one_dim_real_induced_param_pol¶
one_dim_real_induced_param_pol:Param p, Parabolic P->[(Param,ParamPol)] Defined in line number 137.Auxiliary function: List of all modules with infinitesimal character of p, that are induced from a unitary character on the Levi of P.
one_dim_real_induced_param¶
one_dim_real_induced_param:Param p, Parabolic P->[(Param,Param)] Defined in line number 149.Auxiliary function: As previous function, except a list of all parameters occurring as constitutents of such modules.
is_real_induced_from_character_from_P¶
is_real_induced_from_character_from_P:Param p, Parabolic P->bool Defined in line number 158.Decide whether p is the parameter of a (constituent of a) module induced from a unitary character on the real parabolic P.
is_real_induced_from_one_dimensional¶
is_real_induced_from_one_dimensional:Param p->bool Defined in line number 164.Determine whether parameter p is that of a (constituent of a) module (real) induced from a unitary character.
real_induced_from_one_dim¶
real_induced_from_one_dim:Param p->[(Parabolic,Param)] Defined in line number 175.List all one-dimensional unitary parameters pL so that p is real-induced from pL
wf_aqs_param_pol¶
wf_aqs_param_pol:ratvec gamma, Parabolic P->[(Param,ParamPol)] Defined in line number 187.List of all unitary weakly fair Aq(lambda) modules with infinitesimal character gamma, and induced from P.
wf_aqs_param¶
wf_aqs_param:ratvec gamma, Parabolic P->[(Param,Param)] Defined in line number 199.As previous function, except a list of all parameters occurring as constitutents of such modules.
is_unitary_by_cases¶
is_unitary_by_cases:Param p->bool Defined in line number 211.Test whether the irreducible given by a parameter is unitary; if strongly regular, then check if good Aq. Otherwise, check whether it is real or theta induced from a unitary character; if not, compute the hermitian form.
is_unitary_sr¶
is_unitary_sr:Param p->bool Defined in line number 229.Test whether a representation is unitary, checking first whether it is strongly regular.
is_unitary_reduced_with_form¶
is_unitary_reduced_with_form:Param p->(ParamPol,bool) Defined in line number 240.Test whether a representation is unitary, checking first whether it is strongly regular; if not, reducing it in the (weakly) good range, and inducing the hermitian form of the smaller group. This function the hermitian form and a boolian.
is_unitary_reduced¶
is_unitary_reduced:Param p->bool Defined in line number 260.As previous function, but only returns true/false.