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On certain categories of modules for affine Lie algebras

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Abstract.

In this paper, we exploit basic formal variable techniques to study certain categories of modules for an (untwisted) affine Lie algebra , motivated by Chari-Pressley’s work on certain integrable modules. We define and study two categories and of -modules using generating functions, where is proved to contain the well known evaluation modules and to unify highest weight modules, evaluation modules and their tensor product modules. We classify integrable irreducible -modules in categories and 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.

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Acknowledgments.

We would like to thank Professor Vyjayanthi Chari for her interest in this paper and for her expert comments and suggestions, and to thank Professor S. Eswara Rao for informing us some of his closely related work. We are grateful to the referee for giving useful suggestions for improving the organization of the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rutgers University, Camden, NJ, 08102, USA

    Haisheng Li

  2. Department of Mathematics, Harbin Normal University, Harbin, People’s Republic of China

    Haisheng Li

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  1. Haisheng Li
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in final form: 12 November 2003

Partially supported by a NSA grant and a grant from Rutgers Research Council.

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Li, H. On certain categories of modules for affine Lie algebras. Math. Z. 248, 635–664 (2004). https://doi.org/10.1007/s00209-004-0674-8

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  • DOI: https://doi.org/10.1007/s00209-004-0674-8

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