Atlas of Lie Groups and Representations

Documentation contents

Script File

extParamPol.at

implement ParamPol for extended parameters
Source
atlas-scripts/extParamPol.at (434 lines)
Definitions
38
Loads
Loaded by
none of the other all.at files

Definitions in source order

ExtParamPol type

L12
set_type ExtParamPol = (ParamPol P_plus, ParamPol P_minus, ParamPol P_ind)

Fields: P_plus, P_minus, P_ind

(P_plus,P_minus,P_ind)=(\sum_i s_ip_i, \sum_j t_jq_j, \sum_k u_kr_k) <->
\sum_i s_iE(p_i,+) + \sum_j t_j E(q_j,-) + \sum_k u_k E(r_k,ind)
L13

*

L17*(Split s,ExtParamPol(P_plus,P_minus,P_ind)) = ExtParamPol

also in this file at line 35, line 57; also defined in basic.at, complex.at, modules.at, hodge_tensor.at, tits_centralizer.at, stable.at

extParamPol 2 overloads

L20extParamPol (ExtParam E) = ExtParamPol
L28extParamPol (Param p,int type) = ExtParamPol
presumably type is in range {-1,0,1} here

*

L35* (Split s,ExtParam E) = ExtParamPol

also in this file at line 17, line 57; also defined in basic.at, complex.at, modules.at, hodge_tensor.at, tits_centralizer.at, stable.at

+

L37+ (ExtParamPol(P_plus_1,P_minus_1,P_ind_1) ,ExtParamPol (P_plus_2,P_minus_2,P_ind_2) ) = ExtParamPol

also in this file at line 47, line 49; also defined in basic.at, modules.at

-

L42-(ExtParamPol(P_plus_1,P_minus_1,P_ind_1) ,ExtParamPol (P_plus_2,P_minus_2,P_ind_2) ) = ExtParamPol

also defined in basic.at, modules.at

+ 2 overloads

L47+ (ExtParamPol P,[ExtParamPol] Q) = ExtParamPol
L49+ (ExtParamPol P,(Split S,Param p,int type)) = ExtParamPol

also in this file at line 37; also defined in basic.at, modules.at

display

L52display (ExtParamPol(A,B,C)) = void

null_ext_module

L54null_ext_module (RealForm G) = ExtParamPol

*

L57* (ExtParam(ic,,,lambda,theta,,,,,):E,rat r) = ExtParam
scale continuous part (|nu|) of extended parameter by rational factor |r|

also in this file at line 17, line 35; also defined in basic.at, complex.at, modules.at, hodge_tensor.at, tits_centralizer.at, stable.at

deform_unreduced

L60deform_unreduced (Param p, mat delta, int type) = ExtParamPol

deform

L100deform = deform_unreduced@(Param,mat,int)

also in this file at line 159

deform_old

L102deform_old (Param p, mat delta, int type) = ExtParamPol

deform

L159deform (ExtParam E, mat delta) = ExtParamPol

also in this file at line 100

change_nu

L165change_nu (Param p, rat factor, int type) = ExtParamPol
given extended parameter (p,type) multiply nu(p) by rat r
uses finalize_extended

%

L186% (ExtParamPol(P_plus,P_minus,P_ind)) = [(Split,Param,int)]
replace ExtParamPol (P_plus,P_minus,P_ind) with [(s_i,c_i,type_i)]

also defined in basic.at

recursive_deform

L192recursive_deform (Param p, mat delta, int type_p) = ExtParamPol

full_deform

L248full_deform = recursive_deform@(Param,mat,int)

also defined in basic.at

character_formula

L282character_formula (Param p,mat delta,int type) = ExtParamPol

also defined in modules.at

c_form_std_big

L303c_form_std_big = full_deform@(Param,mat,int)
c-form of std module for the extended group is just full_def.

c_form_irreducible_big 2 overloads

L305c_form_irreducible_big (Param p,mat delta, int type,ExtParamPol cf) = ExtParamPol
L329c_form_irreducible_big (Param p,mat delta, int type) = ExtParamPol

c_form_irreducible_big_as_sum_of_standards

L332c_form_irreducible_big_as_sum_of_standards (Param p,mat delta, int type) = ExtParamPol

c_form_irreducible_big_long

L342c_form_irreducible_big_long (Param p,mat delta, int type) = (ExtParamPol ,[(Split,Param),ExtParamPol] ,[(Split,Param),ExtParamPol] ,[(Split,Param),ExtParamPol] ,ExtParamPol )
"big" versions
L413

reduce

L415reduce (ExtParamPol(plus,minus,)) = ParamPol

hermitian_form_irreducible_big

L417hermitian_form_irreducible_big (Param p) = KTypePol

is_unitary_big

L421is_unitary_big (Param p) = bool

is_weakly_unitary_big

L432is_weakly_unitary_big (Param p) = bool
compute Hermitian form on p, and report if it is unitary

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).