New solutions of the Yang-Baxter equation associated with quantised orthosymplectic lie superalgebras

Solutions of the Yang-Baxter equation associated with quantised deformations of the twisted and untwisted general linear, orthogonal and symplectic Lie algebras in the fundamental representations have long been known. The extension of these results to the supersymmetric (or more precisely ℤ2-graded) Lie algebras has been incomplete. The untwisted supersymmetric general linear (i.e. Uq[gl(m|n)(1)]) solutions fall into the class of Perk-Schultz models, but the corresponding results for the untwisted orthosymplectic case Uq[osp(m|n)(1)] and twisted general linear superalgebras Uq[gl(m|n)(2)] were not known. Formal expressions exist but explicit formulae in terms of the matrix elements in the tensor product space on which the solution acts were lacking. Here we will present the spectral parameter dependent R-matrices, which solve the Yang-Baxter equation, associated with the latter quantised superalgebras. After explicitly constructing R-matrix solutions of the spectral parameter dependent Yang-Baxter equation, we find the Bethe ansatz equations associated with the quantised untwisted affine Lie superalgebra Uq[osp(m|n)(1)].