FUNCTION: HekaCharTable - compute the table of characters

CALLING SEQUENCE:

HekaCharTable(n)

HekaCharTable(n, 'index')

HekaCharTable(n, part_1, part_2)

HEKA[HekaCharTable](n)

HEKA[HekaCharTable](n, 'index')

HEKA[HekaCharTable](n, part_1, part_2)

PARAMETERS:

n = any positive integer

part_1, part_2 = any lists denoting partitions

SYNOPSIS:

• The HekaCharTable gives the table of values of irreducible characters on special elements of the Hecke algebra. To every partition (of n) part_2 = [a, b, c, ...] one associates a permutation perm which is a direct product of cycles. The code of perm is [a-1, 0$(a-1), b-1, 0$(b-1), c-1, 0$(c-1), ...]. Then, HekaCharTable(n, part_1, part_2) gives the value of the irreducible character indexed by part_1 on the element part_2.

• HekaCharTable(n) gives the matrix of HekaCharTable(n, part_1, part_2) for all partitions of n (HekaCharTable(n, 'index')). 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 HekaCharTable and another name used in the same session, use the long form HEKA['HekaCharTable'].

EXAMPLES:

> with(HEKA):
> HekaCharTable(3);
 
                            [    2              ]
                            [  q1       q1    1 ]
                            [                   ]
                            [ q2 q1  q1 + q2  2 ]
                            [                   ]
                            [    2              ]
                            [  q2       q2    1 ]
 
> HekaCharTable(3, 'index');
 
                            [[3], [2, 1], [1, 1, 1]]
 
> HekaCharTable(3, [2,1], [3]);
 
                                      q2 q1