B Aneva et al 2008 J. Phys. A: Math. Theor. 41 135201 doi:10.1088/1751-8113/41/13/135201
From quantum affine symmetry to the boundary Askey–Wilson algebra and the reflection equation
B Aneva1, M Chaichian2 and P P Kulish3
Show affiliationsWithin 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.
- PACS
- MSC
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47A75 Eigenvalue problems (See also 49R50)
81R15 Operator algebra methods (See also 46Lxx, 81T05)
15A30 Algebraic systems of matrices (See also 16S50, 20Gxx, 20Hxx)
- Subjects
- Dates
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Issue 13 (4 April 2008)
Received 27 November 2007
Published 14 March 2008
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From quantum affine symmetry to the boundary Askey–Wilson algebra and the reflection equation
B Aneva et al 2008 J. Phys. A: Math. Theor. 41 135201
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