Yang-Baxter R-operators for osp superalgebras

TL;DR

This paper develops a new approach to constructing Yang-Baxter R-operators with orthosymplectic supersymmetry, expressing them via operator-valued Gamma functions, and applies it to explicit low-rank cases.

Contribution

It extends a novel construction method of R-operators to the supersymmetric orthosymplectic case, providing explicit formulas and a simpler derivation of key formulas.

Findings

Explicit R-operators for low-rank osp(n|2m) cases

New derivation of the Shankar-Witten formula for osp

Equivalence of previous and new approaches to R-operator construction

Abstract

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.