We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\mathcal{R}}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of orthosymplectic symmetry. In this approach the orthosymplectic $\hat{\mathcal{R}}$-operator is given by the ratio of two operator valued Euler Gamma-functions. We illustrate this approach by calculating such $\hat{\mathcal{R}}$ operators in explicit form for special cases of the $osp(n|2m)$ 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 $\hat{\mathcal{R}}$-operator and demonstrate the equivalence of the previous approach to the new one in the general case of the $\hat{\mathcal{R}}$-operator invariant under the action of the $osp(n|2m)$ algebra.

我们研究具有正交对称超对称性的Yang-Baxter方程。我们扩展了脊柱和偏瘫构造的新方法$\widehat{\mathcal{[R}}$-具有正交对称和辛对称性的算子到正对称的超对称情况。在这种方法中，正统$\widehat{\mathcal{[R}}$-算子由两个算子值的欧拉伽马函数之比给出。我们通过计算$\widehat{\mathcal{[R}}$ 特殊形式的运算符的显式形式 $Øsp（ñ|\mathrm{2个}米）$代数，特别是在一些低阶情况下。我们还为osp不变式提出了Shankar-Witten类型公式的新颖，更简单，更优雅的推导$\widehat{\mathcal{[R}}$-运算符，并在一般情况下证明先前方法与新方法的等效性 $\widehat{\mathcal{[R}}$-运算符在 $Øsp（ñ|\mathrm{2个}米）$ 代数