Yang-Baxter R-operators for osp superalgebras

We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic R ˆ -operators with orthogonal and symplectic symmetries to the supersymmetric case of orthosymplectic symmetry. In this approach the orthosymplectic R ˆ -operator is given by the ratio of two operator valued Euler Gamma-functions. We illustrate this approach by calculating such R ˆ operators in explicit form for special cases of the osp (n | 2 m) algebra, in particular for a few low-rank cases. We also propose a novel, simpler and more elegant, derivation of the Shankar-Witten type formula for the osp invariant R ˆ -operator and demonstrate the equivalence of the previous approach to the new one in the general case of the R ˆ -operator invariant under the action of the osp (n | 2 m) algebra.