Symmetric function products and plethysms and the boson-fermion correspondence

Abstract

We use the boson-fermion correspondence for S and Q functions to establish some interesting properties concerning outer products and plethysms of S-functions (or Q-functions) by power sum symmetric functions. The techniques which are developed are also applied to computing the inverse Kostka-Foulkes matrix (which is the transition matrix between Hall-Littlewood symmetric functions and S-functions) in some simple cases.