Some remarks on characters of symmetric groups, Schur functions, Littlewood-Richardson and Kronecker coefficients

Abstract

The evaluation of characters of symmetric groups as polynomials in class numbers will be discussed, along with their use in evaluating Kronecker coefficients of both conventional and reduced type. Some properties of the polynomial and quasi-polynomial behaviour of stretched Littlewood-Richardson coefficients and stretched Kronecker coefficients will be pointed out. It will be shown that as an alternative to the Kronecker tableaux that have been used to provide a combinatorial model of a certain restricted class of Kronecker coefficients it is possible to use the hive model that was originally used in the study of Littlewood-Richardson coefficients.