Non-Abelian $SU(3)_k$ anyons: inversion identities for higher rank face models

TL;DR

This paper derives exact inversion identities for transfer matrices in integrable $SU(3)_k$ face models, advancing understanding of their spectral properties and connection to higher rank non-Abelian anyons.

Contribution

It introduces new inversion identities for higher rank face models related to $SU(3)_k$, linking them to the spectral problem of non-Abelian anyons.

Findings

Proves inversion identities using Yang-Baxter and unitarity

Connects identities to Separation of Variables method

Enhances spectral analysis of $SU(3)_k$ models

Abstract

The spectral problem for an integrable system of particles satisfying the fusion rules of $SU(3)_k$ is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused $A_2^{(1)}$ interaction round a face (IRF) model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang-Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the Separation of Variables approach to integrable vertex models.