Weyl-Kac type character formula for admissible representations of Borcherds-Kac-Moody Lie superalgebras

摘要

We prove that Borcherds-Kac-Moody Lie superalgebras yield Weyl-Kac type character formulas for some specific types of admissible representations. Our results generalize the results of Kac and Wakimoto (Proc Natl Acad Sci USA 85:4956-4960, 1988) by extending the Weyl-Kac character formula for integrable irreducible highest weight modules over Kac-Moody algebras to the case of admissible irreducible highest weight modules over Borcherds-Kac-Moody Lie superalgebras.