Bn(1) and A2n(2) reflection K-matrices Original Research Article

We investigate the regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the Bn(1) and A2n(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 Bn(1) models and 2n+1 diagonal solutions for A2n(2) models. It turns out that for each Bn(1) model there exist a diagonal K-matrix with one free parameter. Moreover, a three free parameter general solution exists for the B1(1) model which is the vector representation for the Zamolodchikov–Fateev model.