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}
}