Non-Abelian symmetries of the half-infinite XXZ spin chain

TL;DR

This paper classifies the non-Abelian symmetries of the half-infinite XXZ spin chain under various boundary conditions, introducing new algebraic structures related to integrable boundary symmetries.

Contribution

It provides a comprehensive classification of symmetries for all boundary conditions and introduces two novel algebras associated with specific boundary types.

Findings

Classification of symmetries for all boundary conditions

Introduction of two new symmetry algebras

Explicit Chevalley-type presentations for each case

Abstract

The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an analog of the Chevalley-type presentation is given for the corresponding symmetry algebra. In particular, two new algebras arise that are, respectively, generated by the symmetry operators of the model with triangular and special $U_q(gl_2)-$invariant integrable boundary conditions.