R-matrices and Spectrum of Vertex Models based on Superalgebras

In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated R-matrices are presented in terms of the standard Weyl basis making possible the formulation of the quantum inverse scattering method for these lattice models. This allowed us to derive the eigenvectors and the eigenvalues of the corresponding transfer matrices as well as explicit expressions for the Bethe ansatz equations.