FUNCTION: SgDimRep - compute the dimension of a representation

CALLING SEQUENCE:

SgDimRep(part)

SG[SgDimRep](part)

PARAMETERS:

part = any list denoting a (skew) partition

SYNOPSIS:

• The SgDimRep function computes the dimension of the irreducible representation of index part, for the symmetric group of order the weight of part.

• When part is a skew partition, it computes the dimension of the representation indexed by the skew partition part[1]/part[2].

• Adding the parameter 'q', it computes the specialization of s[part] or s[part[1]/part[2]] in x_1=1, x_2=q, x3=q^2, ...

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

EXAMPLES:

> with(SG):
> SgDimRep([4,4,3,2,1,1,1]);
 
                                  512512
 
> SgDimRep([[4,2,1,1], [2,1]]);
 
                                      30
 
> SgDimRep([[4,2,1,1], [2,1]], 'q');
 
                  2            2        4    3    2
                (q  + q + 1) (q  + 1) (q  + q  + q  + q + 1) q