Journal of Physics A Mathematical and General

Multiparameter dependent solutions of the Yang-Baxter equation

R. B. Zhang

Published May 21, 1991• 5 citations

Abstract

A general method is developed for constructing representations of the Temperley-Lieb algebra, which in turn yield solutions of the Yang-Baxter equation. Several classes of multiparameter dependent R-matrices are obtained using this method, and the connection of the method with quantum groups is discussed.

DOI: 10.1088/0305-4470/24/10/008

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Journal of Physics A Mathematical and General

Multiparameter dependent solutions of the Yang-Baxter equation

R. B. Zhang

Published May 21, 1991• 5 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/24/10/008

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Lidan Gou, Ruihan Zhu

Chinese Physics BFeb 1, 20121 citation

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.

We construct

R

-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They change with the representation of the latter. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.