Abstract
In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra τ. More specifically, we define and study two categories Eτ and Cτ of τ-modules using generating functions, where Eτ is proved to contain the evaluation modules while Cτ contains certain restricted τ-modules, the evaluation modules, and their tensor product modules. Furthermore, we classify the irreducible integrable modules in categories Eτ and Cτ.
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