Representation theory of the reflection equation algebra III: Classification of irreducible representations

TL;DR

This paper classifies all irreducible bounded *-representations of the reflection equation algebra associated with the q-deformation of GL(N,C), advancing the understanding of its representation theory.

Contribution

It develops a highest weight theory and provides a complete classification of irreducible bounded *-representations for the algebra.

Findings

Classification of irreducible bounded *-representations achieved

Development of a highest weight theory for the algebra

Enhanced understanding of the algebra's representation structure

Abstract

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form of highest weight theory and use it to classify the irreducible bounded $*$-representations of the reflection equation algebra.