Classification of Irreducible Nonzero Level Modules with Finite-Dimensional Weight Spaces for Affine Lie Algebras

✍ Scribed by V Futorny; A Tsylke

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 142 KB
• Volume: 238
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8648

✦ Synopsis

We classify the irreducible weight affine Lie algebra modules with finite-dimensional weight spaces on which the central element acts nontrivially. In particular, we show that any such module is a quotient of a generalized Verma module. The classification of such irreducible modules is reduced to the classification of irreducible torsion-free modules for algebras of type A and C which is due to n n Ž . O. Mathieu forthcoming .