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arXiv:hep-th/0204076 · Journal of Physics A Mathematical and General

Solutions of the boundary Yang Baxter equation for arbitrary spin

Gustav W. Delius, Rafael I. Nepomechie

Published Jun 10, 2002• 25 citations
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Abstract

We use boundary quantum group symmetry to obtain recursion formulae which determine nondiagonal solutions of the boundary Yang–Baxter equation (reflection equation) of the XXZ type for any spin j .
DOI
10.1088/0305-4470/35/24/102

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This work concerns studies of boundary integrability of the vertex models from representations of the Temperley–Lieb algebra associated with the quantum group 𝒰 q [ X n ] for the affine Lie algebras X n = , , and . A systematic computation method is used to construct solutions of the boundary Yang–Baxter equations. We find a 2 n 2 + 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 2 n 2 + 2 n + 1 free parameters.
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