Temperley-Lieb K-matrices

This work concerns studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group q[Xn] for the affine Lie algebras Xn = , , and . A systematic computation method is used to construct solutions of the boundary Yang-Baxter e...

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Bibliographic Details
Published in:Journal of statistical mechanics 2013-10, Vol.2013 (10), p.P10021-16
Main Author: Lima-Santos, A
Format: Article
Language:English
Subjects:
Algebra
Boundaries
Lie groups
Mathematical analysis
Mathematical models
Representations
Statistical mechanics
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Summary:This work concerns studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group q[Xn] for the affine Lie algebras Xn = , , and . A systematic computation method is used to construct solutions of the boundary Yang-Baxter equations. We find a 2n2 + 1 free parameter solution for spin-(n − 1 2) and vertex models. It turns out that for spin-n, and vertex models, the solution has 2n2 + 2n + 1 free parameters.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2013/10/P10021