aql.at

aql_verbose

inf_chars_dom_for_L

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 2 overloads

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.

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.

one_dim_params_gamma

List all one-dimensional unitary characters with given
infinitesimal character.

wf_one_dim_params

List all one-dimensional unitary characters, in the weakly fair range,
of L, with given infinitesimal character.

wf_aqs_param_pol

Auxiliary function: List of all unitary weakly fair Aq(lambda) modules
with infinitesimal character of p, and induced from P.

also in this file at line 175

wf_aqs_param

Auxiliary function: As previous function, except a list of all
parameters occurring as constituents of such modules.

also in this file at line 187

is_weakly_fair_Aq_from_P

Decide whether p is the parameter of a (constituent of a) unitary
weakly fair Aq(lambda) induced from parabolic P.

special_theta_stable_parabolics

List all proper theta-stable parabolics for G that are not Borels.

all_wf_Aq_with_ic_of

List all parameters of constituents of weakly fair Aq(lambda) modules with
the same infinitesimal character as p.

is_weakly_fair_Aq

Determine whether parameter p is that of a (constituent of a)
unitary weakly fair Aq(lambda) module.

is_wf_induced_from_one_dim

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

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

Auxiliary function: As previous function, except a list of all
parameters occurring as constituents of such modules.

is_real_induced_from_character_from_P

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

Determine whether parameter p is that of a (constituent of a) module (real)
induced from a unitary character.

real_induced_from_one_dim

List all one-dimensional unitary parameters pL so that p is real-induced
from pL

wf_aqs_param_pol

List of all unitary weakly fair Aq(lambda) modules
with infinitesimal character gamma, and induced from P.

also in this file at line 43

wf_aqs_param

As previous function, except a list of all
parameters occurring as constituents of such modules.

also in this file at line 54

is_unitary_by_cases

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

Test whether a representation is unitary, checking first whether
it is strongly regular.

is_unitary_reduced_with_form

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

As previous function, but only returns true/false.