Atlas of Lie Groups and Representations

Documentation contents

atlas Library · Script File

KL_polynomial_matrices.at

Source
atlas-scripts/KL_polynomial_matrices.at (141 lines)
Definitions
24
Loads
Loaded by
L_packet.at dual.at bigMatrices.at

Definitions in source order

eval

L5eval (i_poly_mat M, int k) = mat

also defined in polynomial.at

permutation

L9permutation ([Param] B1, [Param] B2) = ([int],bool)
map from index in B1 to matching index in B2, and whether it's well defined

also defined in combinatorics.at

KL_P_polynomials

L20KL_P_polynomials (Param p) = i_poly_mat

also in this file at line 35, line 91, line 104

KL_P_polynomials_at_minus_one

L24KL_P_polynomials_at_minus_one (Param p) = mat

also in this file at line 42, line 97, line 112

KL_P_signed_polynomials

L27KL_P_signed_polynomials (Param p) = i_poly_mat

also in this file at line 45, line 115, line 124

KL_P_signed_polynomials_at_minus_one

L32KL_P_signed_polynomials_at_minus_one (Param p) = mat

also in this file at line 54, line 121, line 132

KL_P_polynomials

L35KL_P_polynomials([Param] B) = i_poly_mat

also in this file at line 20, line 91, line 104

KL_P_polynomials_at_minus_one

L42KL_P_polynomials_at_minus_one ([Param] B) = mat

also in this file at line 24, line 97, line 112

KL_P_signed_polynomials

L45KL_P_signed_polynomials ([Param] B) = i_poly_mat

also in this file at line 27, line 115, line 124

KL_P_signed_polynomials_at_minus_one

L54KL_P_signed_polynomials_at_minus_one ([Param] B) = mat

also in this file at line 32, line 121, line 132

KL_Q_polynomials

L57KL_Q_polynomials (Param p) = i_poly_mat

also in this file at line 61, line 138, line 140

transpose
L59

KL_Q_polynomials

L61KL_Q_polynomials ([Param] B) = i_poly_mat

also in this file at line 57, line 138, line 140

twisted versions
L68

final_subset

L70final_subset ([Param] B) = [Param]
this is the twisted analogue of |KL_block@Param|. Originally called
|ext_KL_block| the 'ext_' prefix is superfluous since it is implied by the
presence of |delta|, and is therefore dropped
L74

KL_block

L81KL_block (Param p, mat delta) = ([Param],mat,[vec])
undo signedness of |partial_extended_KL_block|, using a negative index for any
negated poly

KL_P_polynomials

L91KL_P_polynomials (Param p, mat delta) = i_poly_mat

also in this file at line 20, line 35, line 104

KL_P_polynomials_at_minus_one

L97KL_P_polynomials_at_minus_one (Param p, mat delta) = mat

also in this file at line 24, line 42, line 112

KL_P_polynomials

L104KL_P_polynomials ([Param] B_fixed, mat delta) = i_poly_mat

also in this file at line 20, line 35, line 91

KL_P_polynomials_at_minus_one

L112KL_P_polynomials_at_minus_one ([Param] B_fixed, mat delta) = mat

also in this file at line 24, line 42, line 97

KL_P_signed_polynomials

L115KL_P_signed_polynomials (Param p, mat delta) = i_poly_mat

also in this file at line 27, line 45, line 124

KL_P_signed_polynomials_at_minus_one

L121KL_P_signed_polynomials_at_minus_one (Param p, mat delta) = mat

also in this file at line 32, line 54, line 132

KL_P_signed_polynomials

L124KL_P_signed_polynomials([Param] B, mat delta) = i_poly_mat

also in this file at line 27, line 45, line 115

KL_P_signed_polynomials_at_minus_one

L132KL_P_signed_polynomials_at_minus_one([Param] B, mat delta) = mat

also in this file at line 32, line 54, line 121

KL_Q_polynomials 2 overloads

L138KL_Q_polynomials (Param p, mat delta) = i_poly_mat
since there is no "dual_partial_extended_KL_block", define the Q-polynomials
as inverse of the signed P-matrix
L140KL_Q_polynomials ([Param] B, mat delta) = i_poly_mat

also in this file at line 57, line 61

Generated from atlas-scripts at commit 648506c (2026-10-13).