Integrable modules for affine Lie superalgebras

Eswara Rao, Senapathi; Futorny, Vyacheslav

doi:10.1090/S0002-9947-09-04749-7

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.

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