The algebraic Bethe ansatz for rational braid-monoid lattice models Original Research Article

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the Bn, Cnand Dn Lie algebra and by the superalgebra Osp(n||2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvaluesof the transfer matrix associated to the Bn, Cn, Dn, Osp(2nt-1||2), Osp(2||2nt-2), Osp(2nt-2||2) and Osp(1||2n) models. The corresponding Bethe ansatz equations can be formulated in terms of the root structure of the underlying algebra.