Typical irreducible characters of generalized quantum groups

Abstract

We introduce the definition of the typical irreducible modules of the generalized quantum groups, and prove the Weyl–Kac-type formulas of their characters. As a by-product, we obtain the Weyl–Kac-type character formulas of the typical irreducible modules of the quantum superalgebras associated with the basic classical Lie superalgebras, which is explained in Introduction.