Yang-Baxter R-operators for osp superalgebras

Abstract

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.

30 pages

References in corpus (4)

• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• Spinorial R operator and Algebraic Bethe Ansatz
• Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras
• D-dimensional spin projection operators for arbitrary type of symmetry via Brauer algebra idempotents

Cited by in corpus (5)

• Lax Operator and superspin chains from 4D CS gauge theory
• Representations of the Yangians associated with Lie superalgebras $\mathfrak{osp}(1|2n)$
• Representations of the orthosymplectic Yangian
• Orthosymplectic superoscillator Lax matrices
• The split Casimir operator and solutions of the Yang-Baxter equation for the $osp(M|N)$ and $s\ell (M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters