hyperoctahedralGroupTable -- character table of the hyperoctahedral group

Usage:

hyperoctahedralGroupTable(n,F)
Inputs:
- n, an integer, positive
- F, a ring, a field
Outputs:
- an instance of the type CharacterTable,

Description

Returns the character table of the hyperoctahedral group $H_n$ over the field F. The irreducible characters are indexed by bipartitions of $n$, i.e., pairs of partitions of two integers adding up to $n$.

i1 : hyperoctahedralGroupTable(3,QQ)

o1 = Character table over QQ
      
              |   8   6  1   6   3   6   3   8   6   1
     ---------+---------------------------------------
       (3;0)  |   1   1  1   1   1   1   1   1   1   1
     (2,1;0)  |  -1   0  2   0   2   0   2  -1   0   2
        3     |                                     
      (1 ;0)  |   1  -1  1  -1   1  -1   1   1  -1   1
       (2;1)  |   0   1  3  -1   1   1  -1   0  -1  -3
        2     |                                     
      (1 ;1)  |   0  -1  3   1   1  -1  -1   0   1  -3
       (1;2)  |   0   1  3   1  -1  -1  -1   0  -1   3
          2   |                                     
      (1;1 )  |   0  -1  3  -1  -1   1  -1   0   1   3
       (0;3)  |   1   1  1  -1  -1  -1   1  -1   1  -1
     (0;2,1)  |  -1   0  2   0  -2   0   2   1   0  -2
          3   |                                     
      (0;1 )  |   1  -1  1   1  -1   1   1  -1  -1  -1

o1 : CharacterTable

Ways to use hyperoctahedralGroupTable:

hyperoctahedralGroupTable(ZZ,Ring)

For the programmer

The object hyperoctahedralGroupTable is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/BettiCharacters.m2:3859:0.