  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 B_n, C_n and D_n 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
eigenvalues of the transfer matrix associated to the B_n, C_n, D_n,
Osp(2n-1|2), Osp(2|2n-2), Osp(2n-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.
