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In this paper, using generating functions, we study two categories [Figure not available: see fulltext.] and [Figure not available: see fulltext.] of modules for twisted affine Lie algebras [Figure not available: see fulltext.], 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 [Figure not available: see fulltext.]-modules in categories [Figure not available: see fulltext.] and [Figure not available: see fulltext.], where [Figure not available: see fulltext.] is proved to contain the well-known evaluation modules and [Figure not available: see fulltext.] to unify highest weight modules, evaluation modules and their tensor product modules. We determine also the isomorphism classes of those irreducible modules. © 2012 Higher Education Press and Springer-Verlag Berlin Heidelberg.

Certain categories of modules for twisted affine Lie algebras