The Frobenius Characteristic of Character Polynomials

Abstract

Polynomials in an infnite sequence of variables can be evaluated as class functions of symmetric groups on n letters across all n. When they represent characters of families of representations, they are called character polynomials. This article is an introduction to the theory of character polynomials and their Frobenius characteristics. As an application, some generating functions describing the restriction of a polynomial representation of GLn to Sn are obtained.