Atlas of Lie Groups and Representations

Documentation contents

atlas Library · Script File

classical_character_tables.at

type A
Source
atlas-scripts/classical_character_tables.at (282 lines)
Definitions
15
Loads
Loaded by
character_tables_reductive.at springer_tables_reductive.at springer_table_A.at

Definitions in source order

partition_as_irrep_label

L9partition_as_irrep_label (Partition lambda) = string

character_table_S

L12character_table_S (int n) = (CharacterTable,(Partition->int),(Partition->int))

character_table_A

L34character_table_A (RootDatum rd) = (CharacterTable,(Partition->int),(Partition->int))
types B,C
L55

BC_irreps

L57BC_irreps (int n) = [BiPartition]
list [k],..,ones(k)

index_BC_irrep

L61index_BC_irrep = ([BiPartition] -> (BiPartition->int))
for looking up a |BiPartition| among |BC_irreps|, use an adapted comparison:

bipartition_as_irrep_label

L72bipartition_as_irrep_label (BiPartition(lambda,mu)) = string

character_table_B 2 overloads

L75character_table_B (int n) = (CharacterTable,(BiPartition->int),(BiPartition->int))
L99character_table_B (RootDatum rd) = (CharacterTable,(BiPartition->int),(BiPartition->int))

character_table_C 2 overloads

L124character_table_C (int n) = (CharacterTable,(BiPartition->int),(BiPartition->int))
L148character_table_C (RootDatum rd) = (CharacterTable,(BiPartition->int),(BiPartition->int))
type D
L173

D_irreps

L177D_irreps (int n) = [D_irrep]
all irreducible representations of D_n

index_D_irreps

L192index_D_irreps = ([D_irrep]->(D_irrep->int))
In list of |D_irrep|s sorted by ordering of |D_irreps|, look up a |D_irrep|.
The |D_irrep|s in the list are among those produced by |D_irreps|, so that
if unsplit, the larger (for |cmp_partition|) partition comes first; the
second |D_irrep| (whose index we look up) does not have to satisfy this.

irrep_label

L234irrep_label (D_irrep chi) = string

character_table_D 2 overloads

L242character_table_D(int n) = (CharacterTable,(D_class->int),(D_irrep->int))
L263character_table_D(RootDatum rd) = (CharacterTable,(D_class->int),(D_irrep->int))

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