On Integrable Quantum Group Invariant Antiferromagnets

TL;DR

This paper introduces a new integrable open spin chain Hamiltonian invariant under a specific quantum group, exploring its algebraic properties and representation theory implications.

Contribution

It presents a novel integrable Hamiltonian invariant under ${ m U}_ ext{epsilon}(sl(2))$ in nilpotent irreps, using Sklyanin's K-matrices.

Findings

The Hamiltonian is proven to be integrable.

The invariance under ${ m U}_ ext{epsilon}(sl(2))$ is established.

Analysis of the centralizer and representation theory of nilpotent representations.

Abstract

A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\cal U}_{\epsilon}(sl(2))$ transformations in nilpotent irreps for $\epsilon^3=1$. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.