Atlas of Lie Groups and Representations

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atlas Library · Script File

K_types.at

Source
atlas-scripts/K_types.at (67 lines)
Definitions
17
Loads
Loaded by
modules.at print_K_types.at finite_dimensional_signature.at associated_variety_annihilator.at certificate.at tensor_product.at is_normal.at hodge_functions.at K_types_plus.at

Definitions in source order

int_part

L5int_part (KTypePol P) = KTypePol

also defined in basic.at, misc.at

s_part

L7s_part (KTypePol P) = KTypePol

also defined in basic.at, misc.at

branch_std 3 overloads

L10branch_std = (KTypePol,int->KTypePol)
built-in
L11branch_std (KType t, int cut_off) = KTypePol
L12branch_std (ParamPol P, int bound) = KTypePol

branch_irr 2 overloads

L14branch_irr (Param p, int bound) = KTypePol
L17branch_irr (ParamPol P,int bound) = KTypePol

mult_std

L21mult_std (KType p_K,KTypePol P) = int
multiplicity of K-type p_K in standard module p

mult_irr

L25mult_irr (KType p_K,ParamPol P) = int
multiplicity of K-type p_K in irreducible module p

K_signature_irr

L28K_signature_irr (Param p,int bound) = (KTypePol,KTypePol)

signed_mult

L31signed_mult (KType p_K,Param p) = (int,int)

expand 2 overloads

L52expand ([int] v,[KType] K_basis, RealForm G) = KTypePol
K_basis is the basis of a vector space, v is a vector in this basis
return sum_i v[i]*K_types[i]
need G only if #K_basis=0
L56expand ([int] v,[KType] K_basis) = KTypePol
convenience function; gives error if K_basis=[]

also defined in number_theory.at

find

L60find ([KType] list,KType mu) = int
find KType in list of K_types

also defined in basic.at, tits_centralizer.at, nilpotent_orbits.at, cells.at, hodgeParamLaurentPol.at, extended.at, disconnected.at, nilpotent_posets.at, K_types_plus.at

sort_u

L63sort_u ([KType] K_types) = [KType]
sort KTypes uniquely

also defined in sort.at, nilpotent_posets.at

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