From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation

TL;DR

This paper explores the connection between quantum affine symmetry, boundary Askey-Wilson algebra, and reflection equations, providing a framework for solving open driven diffusive systems exactly in stationary states.

Contribution

It constructs boundary symmetry operators from quantum affine algebra representations and links them to the Askey-Wilson algebra and reflection equations, enabling exact solutions.

Findings

Constructed boundary symmetry operators from quantum affine algebra.

Linked Askey-Wilson algebra to reflection equation solutions.

Applied framework to solve open driven diffusive systems in stationary states.

Abstract

Within the quantum affine algebra representation theory we construct linear covariant operators that generate the Askey-Wilson algebra. It has the property of a coideal subalgebra, which can be interpreted as the boundary symmetry algebra of a model with quantum affine symmetry in the bulk. The generators of the Askey-Wilson algebra are implemented to construct an operator valued $K$- matrix, a solution of a spectral dependent reflection equation. We consider the open driven diffusive system where the Askey-Wilson algebra arises as a boundary symmetry and can be used for an exact solution of the model in the stationary state. We discuss the possibility of a solution beyond the stationary state on the basis of the proposed relation of the Askey-Wilson algebra to the reflection equation.