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SG::SgDimRep -- computes the dimension of a representation

Call(s)


SG::SgDimRep(part)

Parameters

part- 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 Functions

SgCharTable

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MuPAD Combinat, an open source algebraic combinatorics package