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