Vertex operator realization of symplectic and orthogonal<b><i>S</i></b>-functions

Abstract

It is shown that symplectic and orthogonal Schur functions can be realized by the action of the modes of certain vertex operators on the function . The properties of these vertex operators allow one to reproduce the basic propreties of these types of symmetric functions. The vertex operator modes are shown to obey free fermionic relations which provide applications such as calculating products and plethysms as well as generating Hirota-type partial differential equations (PDEs) which have symplectic S-functions as functions.