From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and 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 - 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.
Keywords
Cite
@article{arxiv.0804.1623,
title = {From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation},
author = {B. Aneva and M. Chaichian and P. P. Kulish},
journal= {arXiv preprint arXiv:0804.1623},
year = {2008}
}