Transition matrices and kronecker product expansions of symmetric functions

Abstract

The Kronecker product of two homogeneous symmetric polynomials P1 and P2 is defined by means by the Frobenius map by the formula . By using the combinatorial definitions for the transition matrices between the various bases of the space of homogeneous symmetric functions, one obtains a procedure for expanding this Kronecker product. In this paper, we employ this technique to study this expansion for the monomial symmetric functions.