Kac-Wakimoto character formula for the general linear Lie superalgebra

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.

References in corpus (3)

• Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras
• A BGG-type resolution for tensor modules over general linear superalgebra
• Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

Cited by in corpus (3)

• Finite-dimensional half-integer weight modules over queer Lie superalgebras
• Mock Modular Index of M2-M5 Brane System
• Candidate for the crystal $B(-\infty )$ for the queer Lie superalgebra