Irreducible representations for toroidal Lie algebras

Abstract

In this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal Lie algebras. To accomplish this we develop a general theory of Zn-graded Lie algebras with polynomial multiplication. We construct modules by the standard inducing procedure and study their irreducible quotients using the vertex operator technics. © 1999 Academic Press.