On certain categories of modules for affine Lie algebras

Abstract

In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebraĝ by exploiting basic formal variable techniques. We define and study two categories E and C ofĝ-modules using generating functions, where E contains evaluation modules and C unifies highest weight modules, evaluation modules and their tensor product modules, and we classify integrable irreducibleĝ-modules in categories E and C.

Irreducible finite-dimensional representations of equivariant map algebras

“…For a proof in the case dim k V < ∞ see, for example, [Bou58, §7.7, Proposition 8] and observe that irreducibility of V 2 follows from (1). For a proof in general see [Li04,Lemma 2.7]. (3) Suppose L 2 , .…”

Classification of irreducible integrable modules for extended affine Lie algebras with center acting trivially

“…So W will be an irreducible module for g 1 ⊕ g 2 . Therefore W ∼ = W 1 ⊗ W 2 , where W 1 and W 2 are irreducible modules for g 1 and g 2 respectively ( [9] ). Let g ′ = g ′ ss ⊕R, where g ′ and R are Levi and radical part of g ′ .…”

Filtrations and completions of certain positive level modules of affine algebras

“…It is however, not very difficult to see that such a tensor product never contains a copy of a highest weight module. In addition, the corresponding classical situation which was studied in [7] and more recently in [1,18] did not exclude the possibility that such tensor products might in fact be irreducible.…”