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Characters of (relatively) integrable modules over affine Lie superalgebras

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Japanese Journal of Mathematics Aims and scope

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 \({\mathfrak{g}}\). The problem consists of two parts. First, it is the reduction of the problem to the \({\overline{\mathfrak{g}}}\)-module F(L), where \({\overline{\mathfrak{g}}}\) is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight \({\overline{\mathfrak{g}}}\)-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 \({\mathfrak{g}}\)-modules when \({\mathfrak{g}}\) is basic, and all maximally atypical non-critical integrable \({\mathfrak{g}}\)-modules when \({\mathfrak{g}}\) is affine with non-zero dual Coxeter number.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Maria Gorelik

  2. Department of Mathematics, 2-178, Massachusetts Institute of Technology, Cambridge, MA, 02139-4307, USA

    Victor G. Kac

Authors
  1. Maria Gorelik
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  2. Victor G. Kac
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Correspondence to Maria Gorelik.

Additional information

Communicated by: Yasuyuki Kawahigashi

Maria Gorelik: Supported in part by BSF Grant No. 711623.

Victor G. Kac: Supported in part by Simons fellowship.

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Gorelik, M., Kac, V.G. Characters of (relatively) integrable modules over affine Lie superalgebras. Jpn. J. Math. 10, 135–235 (2015). https://doi.org/10.1007/s11537-015-1464-2

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  • DOI: https://doi.org/10.1007/s11537-015-1464-2

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