SG::SgDimRep --
computes the dimension of a representation
Call(s)
SG::SgDimRep(part)
Parameterspart | - | any list denoting a (skew) partition |
Introduction
The SG::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
x1=1, x2=q, ....
Example 1>> muEC::SG::SgDimRep( [4,4,3,2,1,1,1] );
512512
>> muEC::SG::SgDimRep( [[4,2,1,1], [2,1]] );
30
>> muEC::SG::SgDimRep([[4,2,1,1], [2,1]], q);
2 2 2 3 4
q (q + q + 1) (q + 1) (q + q + q + q + 1)
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package