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 script G sign ̂, motivated by Chari-Pressley's work on certain integrable modules. We define and study two categories ε and C of script G sign ̂-modules using generating functions, where ε 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 script G sign ̂-modules in categories ε 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.

Original languageEnglish (US)
Pages (from-to)635-664
Number of pages30
JournalMathematische Zeitschrift
Volume248
Issue number3
DOIs
StatePublished - Nov 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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