Characters of (relatively) integrable modules over affine Lie superalgebras
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11537_2015_Article_1464.pdf
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Author(s)
Gorelik, Maria
Kac, Victor
Date Issued
June 2015
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s11537-015-1464-2
