FUNCTION: GlDimRep - compute the dimension of a representation

CALLING SEQUENCE:

GlDimRep(part)

CLG[GlDimRep](part)

PARAMETERS:

part = any list denoting a (skew) partition

SYNOPSIS:

• The GlDimRep function computes the dimension of the irreducible representation of index part, for the linear group of order _CLGn.

• 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, ..., x_n=q^{n-1}.

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

EXAMPLES:

> with(CLG):
> GlDimRep([2,2,1]);
 
                                      75
 
> GlDimRep([[2,2,1], [1,1]]);
 
                                      50
 
> GlDimRep([[3,1,1], [2,1]], 'q');
 
                             4    3    2         2
                           (q  + q  + q  + q + 1)