English

Kac-Wakimoto character formula for the general linear Lie superalgebra

Representation Theory 2016-01-20 v1 Mathematical Physics Combinatorics math.MP

Abstract

Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the general linear Lie superalgebra gl(m|n). 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 using the Kac-Wakimoto character formula.

Keywords

Cite

@article{arxiv.1310.3798,
  title  = {Kac-Wakimoto character formula for the general linear Lie superalgebra},
  author = {Michael Chmutov and Crystal Hoyt and Shifra Reif},
  journal= {arXiv preprint arXiv:1310.3798},
  year   = {2016}
}