Atlas of Lie Groups and Representations

Documentation contents

atlas Library · Script File

classical_W_classes_and_reps.at

conjugacy classes and representations of classical Weyl groups
this file consists mainly of some union types to
aggregate A/BC/D constructions into a uniform type
see character_tables.at
springer_tables.at
see character_table_*.at (A,B,C,D,E,F,G)
springer_table_*.at (A,BC,D,E,F,G)

functions to extract form the union; for user convenience only, for
programming purpusos always use discrimination clauses (case..esac as below)
Source
atlas-scripts/classical_W_classes_and_reps.at (101 lines)
Definitions
15
Loads
Loaded by
classical_character_tables.at

Definitions in source order

split_class

L18split_class (D_class c) = (Partition,bool)

unsplit_class

L21unsplit_class(D_class c) = Signed_cycles
string representations
L25

parts_string

L27parts_string (Partition lambda) = string

also in this file at line 29

sign_string

L28sign_string (bool s) = string

parts_string

L29parts_string (Partition lambda) = string
partition without brackets

also in this file at line 27

cycles_string 2 overloads

L32cycles_string ([int,bool] cycles) = string
|cycles@(Partition,Partition)| tacks booleans one cycle lengths, the do this:
L42cycles_string (D_class c) = string
some cases special to type D:
L49

is_split

L51is_split(D_class c) = bool

also in this file at line 65; also defined in basic.at

split_and_unsplit_classes

L54split_and_unsplit_classes([D_class] list) = (([Partition,bool],[int]),([Signed_cycles],[int]))

is_split

L65is_split(D_irrep pi) = bool

also in this file at line 51; also defined in basic.at

split_irrep

L68split_irrep (D_irrep pi) = (Partition,bool)

unsplit_irrep

L71unsplit_irrep (D_irrep pi) = (Partition,Partition)

split_and_unsplit_reps

L75split_and_unsplit_reps([D_irrep] list) = (([Partition,bool],[int]), ([Partition,Partition],[int]))

index_D_reps 2 overloads

L87index_D_reps([D_irrep] L) = (D_irrep->int)
curried first
L101index_D_reps ([D_irrep] L,D_irrep rep) = int

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