On representations of $U'_qso_n$

TL;DR

This paper investigates the representations of the non-standard quantum algebra $U'_qso_n$, classifying finite-dimensional modules for generic $q$ and exploring new results for roots of unity, including self-adjoint representations.

Contribution

It introduces a Verma module approach to classify representations of $U'_qso_n$, extending known results to roots of unity and self-adjoint cases.

Findings

Classified finite-dimensional modules for generic $q$

Extended classification to roots of unity

Identified self-adjoint representations on Hilbert spaces

Abstract

We study representations of the non-standard quantum deformation $U'_qso_n$ of $Uso_n$ via a Verma module approach. This is used to recover the classification of finite-dimensional modules for $q$ not a root of unity, given by classical and non-classical series. We obtain new results at roots of unity, in particular for self-adjoint representations on Hilbert spaces.