B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices

Details B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices

2002-10-18

arxiv.org/abs/nlin/0210046v1

Nucl.Phys. B654 (2003) 466-480; Nucl.Phys. B654 (2003) 481-482

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, LaTex

Scientific paper

10.1016/S0550-3213(03)00042-7

We investigate the regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $B_{n}^{(1)}$ and $A_{2n}^{(2)}$ affine Lie algebras. In both class of models we find two general solutions with $n+1$ free parameters. In addition, we have find $2n-1$ diagonal solutions for $B_{n}^{(1)}$ models and $2n+1$ diagonal solutions for $% A_{2n}^{(2)}$ models. It turns out that for each $B_{n}^{(1)}$ model there exist a diagonal K-matrix with one free parameter. Moreover, a three free parameter general solution exists for the $B_{1}^{(1)}$ model which is the vector representation for the Zamolodchikov-Fateev model.

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