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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Graded level zero integrable representations of affine Lie algebras


Authors: Vyjayanthi Chari and Jacob Greenstein
Journal: Trans. Amer. Math. Soc. 360 (2008), 2923-2940
MSC (2000): Primary 17B67
Published electronically: December 11, 2007
MathSciNet review: 2379781
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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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Additional Information

Vyjayanthi Chari
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: vyjayanthi.chari@ucr.edu

Jacob Greenstein
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: jacob.greenstein@ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04394-2
PII: S 0002-9947(07)04394-2
Received by editor(s): February 23, 2006
Published electronically: December 11, 2007
Additional Notes: This work was partially supported by the NSF grant DMS-0500751
Article copyright: © Copyright 2007 American Mathematical Society