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

 

Integrable modules for affine Lie superalgebras


Authors: Senapathi Eswara Rao and Vyacheslav Futorny
Journal: Trans. Amer. Math. Soc. 361 (2009), 5435-5455
MSC (2000): Primary 17B67
Published electronically: May 26, 2009
MathSciNet review: 2515818
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Abstract: Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type $ A(m,n)^{\hat{}}$ and $ C(n)^{\hat{}}$ using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto.


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Additional Information

Senapathi Eswara Rao
Affiliation: Tata Institute of Fundamental Research, Mumbai, India
Email: senapati@math.tifr.res.in

Vyacheslav Futorny
Affiliation: Institute of Mathematics, University of São Paulo, Caixa Postal 66281 CEP 05315-970, São Paulo, Brazil
Email: futorny@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04749-7
PII: S 0002-9947(09)04749-7
Received by editor(s): October 18, 2007
Published electronically: May 26, 2009
Additional Notes: The second author was supported in part by the CNPq grant 307812/2004-9 and by the Fapesp grant 2005/60337-2.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.