A new current algebra and the reflection equation

TL;DR

This paper introduces a new current algebra and demonstrates its isomorphism with the quantum reflection algebra for $U_q(\\hat{sl_2})$, linking them to the q-Onsager algebra, thus expanding the algebraic framework in quantum integrable systems.

Contribution

It establishes an explicit isomorphism between the quantum reflection algebra and a newly defined current algebra, connecting them to the q-Onsager algebra.

Findings

Explicit algebra isomorphism between quantum reflection algebra and current algebra

Identification of these algebras as realizations of q-Onsager algebra

New insights into algebraic structures in quantum integrable models

Abstract

We establish an explicit algebra isomorphism between the quantum reflection algebra for the $U_q(\hat{sl_2})$ R-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal algebras (q-Onsager).