On certain categories of modules for affine Lie algebras

In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebra $\widehat{\text{g}}$ by exploiting basic formal variable techniques. We define and study two categories $\mathcal{E}$ and $\mathcal{C}$ of $\widehat{\text{g}}$-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 $\widehat{\text{g}}$-modules in categories $\mathcal{E}$ and $\mathcal{C}$.