From quantum affine symmetry to the boundary Askey–Wilson algebra and the reflection equation

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.