Introduction

Abstract

Recently there has been a renewed interest in representations related to the study of Kac-Moody algebras, loop algebras, the Virasoro algebra and the associated groups (see for example [P-S], [K-R], [G-W] and [Ar]). These groups appear naturally in quantum theory with infinitely many degrees of freedom, i.e. in canonical quantum field theory, string theory, statistical quantum physics and soliton theory. The renewed interest comes partly from the many fruitful applications in physics and partly, or rather basically, from the mathematical success in dealing with infinite dimensional Lie algebras.