We prove complete reducibility for an integrable module for an affine Lie algebra where the canonical central element acts non-trivially. We further prove that integrable modules does not exists for most of the superaffine Lie algebras where the center acts non-trivially.
A new family of irreducible, integrable modules for affine Lie algebras
โ Scribed by Vyjayanthi Chari; Andrew Pressley
- Publisher
- Springer
- Year
- 1987
- Tongue
- English
- Weight
- 861 KB
- Volume
- 277
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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 th
We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types A ลฝ1. , B ลฝ1. , C ลฝ1. , D ลฝ1. , A ลฝ2. , A ลฝ2. , and D ลฝ2. . We find a special sequence of affine Weyl group elements for the selected perfect crystal, and show that if the highest weight is lโณ , the Dem
Using Littelmann's path model for highest weight representations of KacแMoody algebras, we obtain explicit combinatorial expressions for certain specialized characters of all Demazure modules of A ลฝ1. and A ลฝ2. .