arXiv:nlin/0412058 · Journal of Statistical Mechanics Theory and Experiment

On , , , , , , and reflectionK-matrices

R. Malara, A. Lima-Santos

Published Sep 26, 2006• 32 citations

Abstract

We present the classification of the most general regular solutions to the boundary Yang–Baxter equations for vertex models associated with non-exceptional affine Lie algebras. Reduced solutions found by applying a limit procedure to the general solutions are discussed. We also present the list of diagonal K -matrices. Special cases are considered separately.

DOI: 10.1088/1742-5468/2006/09/p09013

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arXiv:nlin/0412058 · Journal of Statistical Mechanics Theory and Experiment

On , , , , , , and reflectionK-matrices

R. Malara, A. Lima-Santos

Published Sep 26, 2006• 32 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1742-5468/2006/09/p09013

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R

matrices containing several free-parameters. The corresponding reflection

K

matrices, solutions of the boundary Yang-Baxter equation, were also found and classified. We found that there are three different families of regular

K

matrices, regardless of what

R

matrix we choose.

This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group

{\cal U}_{q}[X_{n}]

for the affine Lie algebras

X_{n}

A_{1}^{(1)}

B_{n}^{(1)}

C_{n}^{(1)}

and

D_{n}^{(1)}

. A systematic computation method is used to constructed solutions of the boundary Yang-Baxter equations. We find a

2n^{2}+1

free parameter solution for $A_{1}^{(1)} $ spin-

(n-1/2)

and $ C_{n}^{(1)}$ vertex models. It turns that for $A_{1}^{(1)} $ spin-

n

, $ B_{n}^{(1)}$ and

D_{n}^{(1)}

vertex models, the solution has

2n^{2}+2n+1

free parameters.

On the multiparametric

{\mathcal{U}}_{q}[{D}_{n+1}^{(2)}]

vertex model