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Journal of Physics A Mathematical and General

General Yang-Baxterization of reflection equations and general K-matrices of An-1vertex models

Hong‐Chen Fu, Mo‐Lin Ge

Published Jul 7, 1994• 3 citations
Publisher

Abstract

General Yang-Baxterization of reflection equations for R with two distinct eigenvalues is presented. This procedure is used to construct reflection K-matrices of reflection equations for the A n-1 vertex models. (Diagonal) K-matrices by de Vege and Gonzalez-Ruiz(1993) for the A n-1 vertex model are reproduced. Furthermore, some new off-diagonal K-matrices for the A n-1 vertex model are obtained.

DOI
10.1088/0305-4470/27/13/020

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General Yang-Baxterization of reflection equations for R with two distinct eigenvalues is presented. This procedure is used to construct reflection K-matrices of reflection equations for the A n-1 vertex models. (Diagonal) K-matrices by de Vege and Gonzalez-Ruiz(1993) for the A n-1 vertex model are reproduced. Furthermore, some new off-diagonal K-matrices for the A n-1 vertex model are obtained.
On the multiparametric Uq[Dn+1(2)]{\mathcal{U}}_{q}[{D}_{n+1}^{(2)}]Uq​[Dn+1(2)​] vertex model
In this work, we employ the algebraic-differential method recently developed by the author to solve the Yang-Baxter equation for arbitrary fifteen-vertex models satisfying the ice-rule. We show that there are four different families of such regular RRR matrices containing several free-parameters. The corresponding reflection KKK matrices, solutions of the boundary Yang-Baxter equation, were also found and classified. We found that there are three different families of regular KKK matrices, regardless of what RRR matrix we choose.