Certain categories of modules for twisted affine Lie algebras

Abstract

In this paper, using generating functions, we study two categories ϵ and \varphi of modules for twisted affine Lie algebras \widehat{\mathfrak{g}}[σ], which were firstly introduced and studied for untwisted affine Lie algebras by H. -S. Li [Math Z, 2004, 248: 635-664]. We classify integrable irreducible \widehat{\mathfrak{g}}[σ]-modules in categories ϵ and \varphi, where ϵ is proved to contain the well-known evaluation modules and \varphi to unify highest weight modules, evaluation modules and their tensor product modules. We determine also the isomorphism classes of those irreducible modules.

Keywords

Twisted affine Lie algebra / module / category

References

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