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SYMF::SfCCProd -- computes the conjugacy class product of symmetric functions

Call(s)


SYMF::SfCCProd(sf1,sf2)

Parameters

sf1, sf2- any symmetric functions

Introduction

The SYMF::SfCCProd function computes the conjugacy class product of symmetric functions sf1 and sf2. This product is defined, on the Schur basis, to be

s[lambda] x s[mu] = 0 (lambda <> mu),
s[lambda] x s[lambda] = s[lambda]/f(lambda),
in which f(lambda) stands for the number of standard tableaux of shape lambda.

The result is expressed in the basis of Schur functions.

Example 1

>> muEC::SYMF::SfCCProd(s^2*s[2,1,1] + s[3,1], q*s[2,1,1]);
                                 2
                              q s  s[2, 1, 1]
                              ---------------
                                     3

Related Functions

TYP::Sf

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MuPAD Combinat, an open source algebraic combinatorics package