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Kac-Wakimoto character formula for the general linear Lie superalgebra (1310.3798v1)
Published 14 Oct 2013 in math.RT, math-ph, math.CO, and 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.