FUNCTION: SgCharTable - compute the table of characters

CALLING SEQUENCE:

SgCharTable(n)

SgCharTable(n, 'index')

SgCharTable(n, part_1, part_2)

SG[SgCharTable](n)

SG[SgCharTable](n, 'index')

SG[SgCharTable](n, part_1, part_2)

PARAMETERS:

n = any positive integer denoting the degree of a symmetric group

part_1, part_2 = any lists denoting partitions

SYNOPSIS:

• The SgCharTable gives the table of characters for the symmetric group of order n. Let t be this matrix, part_1, part_2 be two partitions of n, of index i, j in the list of partitions SgCharTable(n, 'index'), then t[i,j] is equal to the value of the irreducible character of index part_1 on the conjugacy class indexed by part_2.

• Partitions indexing rows and columns are also given by PART[ListPart](n).

• One may extract some rows or columns by the linalg[row] and linalg[col] commands of the linalg package.

• Whenever there is a conflict between the function name SgCharTable and another name used in the same session, use the long form SG['SgCharTable'].

EXAMPLES:

> with(SG):
> SgCharTable(3);
 
                                 [  1   1  1 ]
                                 [           ]
                                 [ -1   0  2 ]
                                 [           ]
                                 [  1  -1  1 ]
 
> SgCharTable(3, 'index');
 
                            [[3], [2, 1], [1, 1, 1]]
 
> SgCharTable(3, [2,1], [1,1,1]);
 
                                       2