Classification of Finite Dimensional Irreducible Representations of Generalized Quantum Groups via Weyl Groupoids

TL;DR

This paper classifies finite-dimensional irreducible highest weight modules of certain generalized quantum groups with infinite positive parts, expanding understanding of their representation theory.

Contribution

It introduces a classification method for finite-dimensional irreducible modules of generalized quantum groups with specific root system properties.

Findings

Complete classification of such modules under given conditions

Identification of the structure of modules related to Weyl groupoids

Extension of representation theory for generalized quantum groups

Abstract

We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.