Characters of (relatively) integrable modules over affine Lie superalgebras
Author(s)
Gorelik, Maria; Kac, Victor
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In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number.
Date issued
2015-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Japanese Journal of Mathematics
Publisher
Springer Japan
Citation
Gorelik, Maria, and Victor G. Kac. “Characters of (Relatively) Integrable Modules over Affine Lie Superalgebras.” Japanese Journal of Mathematics 10.2 (2015): 135–235.
Version: Author's final manuscript
ISSN
0289-2316
1861-3624