FUNCTION: SfCCProd - compute the conjugacy class product of symmetric functions

CALLING SEQUENCE:

SfCCProd(sf_1, sf_2, b_1, b_2)

SYMF[SfCCProd](sf_1, sf_2, b_1, b_2)

PARAMETERS:

sf_1, sf_2 = any symmetric functions

b_1, b_2 = any strings denoting names of known bases

SYNOPSIS:

• The SfCCProd function computes the conjugacy class product of symmetric functions sf_1 and sf_2. This product is defined, on the Schur basis, to be s_lambda * s_mu = 0 (lambda != mu), s_lambda * s_lambda = 1/f(lambda) * s_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.

• In the case that sf_1 and sf_2 are solely expressed in the basis b_1 and b_2, one may specify these bases.

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

EXAMPLES:

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