Certain categories of modules for twisted affine Lie algebras

In this paper, using generating functions, we study two categories ? and ? of modules for twisted affine Lie algebras 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 g^σ]-modules in categories ? and ?, where ? is proved to contain the well-known evaluation modules and ? to unify highest weight modules, evaluation modules and their tensor product modules. We determine also the isomorphism classes of those irreducible modules.