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Yang-Baxter R-operators for osp superalgebras
Nuclear Physics B ( IF 2.5 ) Pub Date : 2021-02-25 , DOI: 10.1016/j.nuclphysb.2021.115355
A.P. Isaev , D. Karakhanyan , R. Kirschner

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



中文翻译:

osp超级代数的Yang-Baxter R-运算符

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[Rˆ-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[Rˆ-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[Rˆ 特殊形式的运算符的显式形式 Øspñ|2个代数,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[Rˆ-运算符,并在一般情况下证明先前方法与新方法的等效性 [Rˆ-运算符在 Øspñ|2个 代数

更新日期:2021-03-01
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