On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices

Abstract

This work concerns the boundary integrability of the spin-s ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented. It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free parameters. Moreover, some particular solutions are discussed.

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• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
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Cited by in corpus (5)

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• Universal Bethe ansatz solution for the Temperley-Lieb spin chain
• Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries
• Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
• On the ${\mathcal{U}}_q[osp(1|2)]$ Temperley-Lieb model