On certain categories of modules for affine Lie algebras

In this paper, we exploit basic formal variable techniques to study certain categories of modules for an (untwisted) affine Lie algebra (g) over cap, motivated by Chari-Pressley's work on certain integrable modules. We define and study two categories E and C of (g) over cap -modules using generating functions, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modules and their tensor product modules. We classify integrable irreducible (g) over cap -modules in categories E and C and we determine the isomorphism classes of those irreducible modules. Finally we prove a result that relates fusion rules in the context of vertex operator algebras with integrable irreducible modules of Chari-Pressley.