On certain categories of modules for affine Lie algebras

Abstract

In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebra $\hat{\g}$ by exploiting basic formal variable techniques. We define and study two categories ${\mathcal{E}}$ and ${\mathcal{C}}$ of $\hat{\g}$-modules using generating functions, where ${\mathcal{E}}$ includes evaluation modules and ${\mathcal{C}}$ unifies highest weight modules, evaluation modules and their tensor product modules, and we classify integrable irreducible $\hat{\g}$-modules in categories ${\mathcal{E}}$ and ${\mathcal{C}}$.