Center of quantum group in roots of unity and the restriction of integrable models

TL;DR

This paper explores the relationship between the extended center of quantum groups at roots of unity and the restricted $XXZ$ model, providing explicit operators and verifying their formulas for specific cases.

Contribution

It establishes a connection between quantum group centers at roots of unity and restricted integrable models, offering explicit operator formulas and conjectures for general cases.

Findings

Explicit operators respecting model restrictions are derived.

Formulas verified for third-degree roots.

Conjectures proposed for general roots case.

Abstract

We show the connection between the extended center of the quantum group in roots of unity and the restriction of the $XXZ$ model. We also give explicit expressions for operators that respect the restriction and act on the state space of the restricted models. The formulas for these operators are verified by explicit calculation for third-degree roots; they are conjectured to hold in the general case.