论文标题
Yang-Baxter R-operators for OSP Superalgebras
Yang-Baxter R-operators for osp superalgebras
论文作者
论文摘要
我们研究具有正置超对称性的杨巴克斯特方程。我们扩展了旋转器和元位$ \ hat {\ cal r} $的新方法 - 具有正交和符号对称性的运算符与正交对称性的超对称情况。在这种方法中，正交$ \ hat {\ cal r} $ - 运算符由两个操作员的比例给出，两个操作员的比例。我们通过计算出$ osp（n | 2m）$ algebra的特殊情况的明确表格的这种$ \ hat {\ cal r} $运算符来说明这种方法，尤其是在一些低级别的情况下。 We also propose a novel, simpler and more elegant, derivation of the Shankar-Witten type formula for the $osp$ invariant $\hat{\cal R}$-operator and demonstrate the equivalence of the previous approach to the new one in the general case of the $\hat{\cal R}$-operator invariant under the action of the $osp(n|2m)$ algebra.
We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\cal R}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of orthosymplectic symmetry. In this approach the orthosymplectic $\hat{\cal R}$-operator is given by the ratio of two operator valued Euler Gamma-functions. We illustrate this approach by calculating such $\hat{\cal R}$ 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 $\hat{\cal R}$-operator and demonstrate the equivalence of the previous approach to the new one in the general case of the $\hat{\cal R}$-operator invariant under the action of the $osp(n|2m)$ algebra.
