One of the fundamental problems in Lie theory is the determination of the weight multiplicities of the irreducible highest weight representations of a Lie algebra. The generating function of the multiplicities is called the character of the representation. This project will consider characters of the irreducible highest weight representations of certain infinite dimensional Lie algebras and superalgebras. Specifically, the principal investigator will examine these characters for affine Lie algebras, Virasoro algebras, the Neveu-Schwarz algebras and the Ramond algebras.
