Executive Summary : | The determination of complex finite-dimensional simple Lie algebra characters dates back to the early 20th century and was primarily carried out by Hermann Weyl. The Weyl-Kac character formula for Kac-Moody algebras was studied with two restrictions: symmetrizablity for Kac-Moody algebras and integrability for the highest weight representations. Kac and Wakimoto introduced admissible weights, which are integrable with respect to a sub root system of a given Kac-Moody algebra. They proved that admissible representations of affine Lie algebras satisfy a Weyl-Kac type character formula. Kumar and Mathieu proved the Weyl-Kac character formula for arbitrary Kac-Moody algebras, but finding character formulas for arbitrary irreducible highest weight modules over Kac-Moody algebras remains a challenging problem. This highlights the importance of proving the character formula for various classes of representations. The main goal of this proposal is to understand the unique factorization property of the various categories of representations of BKM superalgebras by proving the character formula for the respective category of representations. |