Integrable modules for affine Lie superalgebras
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- by Senapathi Eswara Rao and Vyacheslav Futorny PDF
- Trans. Amer. Math. Soc. 361 (2009), 5435-5455 Request permission
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.References
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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
- MR Author ID: 238132
- Email: futorny@ime.usp.br
- 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.
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 5435-5455
- MSC (2000): Primary 17B67
- DOI: https://doi.org/10.1090/S0002-9947-09-04749-7
- MathSciNet review: 2515818