Graded level zero integrable representations of affine Lie algebras

Chari, Vyjayanthi; Greenstein, Jacob

doi:10.1090/S0002-9947-07-04394-2

Graded level zero integrable representations of affine Lie algebras
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by Vyjayanthi Chari and Jacob Greenstein PDF

Trans. Amer. Math. Soc. 360 (2008), 2923-2940 Request permission

Abstract:

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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