Kac-Wakimoto character formula for the general linear Lie superalgebra

Michael Chmutov, Crystal Hoyt, Shifra Reif

Published 2013-10-14Version 1

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.