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

Abstract

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.