Typical Irreducible Characters of Generalized Quantum Groups

TL;DR

This paper defines typical irreducible modules for generalized quantum groups and proves Weyl-Kac-type formulas for their characters, extending to quantum superalgebras related to classical Lie superalgebras.

Contribution

It introduces the concept of typical irreducible modules for generalized quantum groups and establishes their character formulas, including applications to quantum superalgebras.

Findings

Weyl-Kac-type character formulas for typical modules

Extension of formulas to quantum superalgebras

New framework for irreducible modules in 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.