The Highest Weight Property for the $SU_{q}(n)$ Invariant Spin Chains

TL;DR

This paper explores the algebraic structure of $SU_q(n)$ invariant spin chains, deriving generators, relations, and eigenvectors, revealing their highest weight vector nature within the quantum group framework.

Contribution

It introduces a method to obtain $SU_q(n)$ generators and relations from Yang-Baxter operators and characterizes eigenvectors as highest weight vectors.

Findings

Generators derived as spectral limits of Yang-Baxter operators

Commutation and Serre relations obtained from Yang-Baxter equations

Eigenvectors identified as highest weight vectors

Abstract

The $SU_{q}(n)$ generators are obtained as large spectral parameter limit of the Yang-Baxter operators in the integrable $SU_{q}(n)$ invariant vertex model. The commutation relations, including Serre relations, are obtained as limits of the Yang-Baxter equations. The recently found eigenvectors of the $SU_{q}(n)$ invariant spin chains are shown to be Highest Weight vectors of the corresponding quantum group.