The representations of quantized walled Brauer algebras

TL;DR

This paper establishes criteria for the semisimplicity of quantized walled Brauer algebras and classifies their simple modules over any field, advancing understanding of their algebraic structure.

Contribution

It provides a new criterion for semisimplicity and a classification of simple modules for quantized walled Brauer algebras over arbitrary fields.

Findings

Criterion for semisimplicity established

Complete classification of simple modules provided

Applicable over any field

Abstract

In this paper, we give a criterion on the semisimplicity of quantized walled Brauer algebras $\mathscr B_{r,s}$ and classify its simple modules over an arbitrary field $\kappa$.