The kac–wakimoto character formula for the general linear lie Superalgebra

Michael Chmutov, Crystal Hoyt, Shifra Reif

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We prove the Kac–Wakimoto character formula for the general linear Lie superalgebra gl(m|n), which was conjectured by Kac and Wakimoto in 1994. This formula specializes to the well-known Kac–Weyl character formula when the modules are typical and to the Weyl denominator identity when the module is trivial. We also prove a determinantal character formula for KW-modules. In our proof, we demonstrate how to use odd reflections to move character formulas between the different sets of simple roots of a Lie superalgebra. As a consequence, we show that KW-modules are precisely Kostant modules, which were studied by Brundan and Stroppel, thus yielding a simple combinatorial defining condition for KW-modules and a classification of these modules.

Original languageEnglish (US)
Pages (from-to)1419-1452
Number of pages34
JournalAlgebra and Number Theory
Volume9
Issue number6
DOIs
StatePublished - Sep 22 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
©2015 Mathematical Sciences Publishers.

Keywords

  • Character formulas
  • Kazhdan–Lusztig polynomials
  • Lie superalgebras
  • Tame modules

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