Fuzzy Torus via q-Parafermion

TL;DR

This paper reinterprets the fuzzy torus as a q-deformed parafermion, classifies its Hermitian representations, and introduces new finite-dimensional representations for roots of unity.

Contribution

It provides a new perspective on the fuzzy torus by linking it to q-parafermions and classifies its Hermitian representations, including novel finite-dimensional cases.

Findings

Classification of Hermitian representations including Fock-type and new finite-dimensional ones.

Introduction of finite-dimensional representations for q as a root of unity.

Reinterpretation of the fuzzy torus in terms of q-parafermions.

Abstract

We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out. The result involves Fock-type representations and new finite dimensional representations for q being a root of unity as well as already known finite dimensional ones.