Graded level zero integrable representations of affine Lie algebras

Details Graded level zero integrable representations of affine Lie algebras Graded level zero integrable representations of affine Lie algebras

2006-02-23

arxiv.org/abs/math/0602514v2

Trans. of the AMS 360 (2008), no. 6, 2923--2940

Mathematics

Representation Theory

17 pages; referee's suggestions incorporated; main result extends to non-simply laced case

Scientific paper

10.1090/S0002-9947-07-04394-2

We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that an indecomposable object has finitely many simple constituents which are non-trivial as modules over the corresponding loop algebra. Moreover, any object in this category is a direct sum of indecomposables only finitely many of which are non-trivial. We obtain a parametrization of blocks in this category.

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