YangBaxter Roperators for osp superalgebras
Abstract
We study YangBaxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic R ˆ operators with orthogonal and symplectic symmetries to the supersymmetric case of orthosymplectic symmetry. In this approach the orthosymplectic R ˆ operator is given by the ratio of two operator valued Euler Gammafunctions. We illustrate this approach by calculating such R ˆ operators in explicit form for special cases of the osp (n  2 m) algebra, in particular for a few lowrank cases. We also propose a novel, simpler and more elegant, derivation of the ShankarWitten type formula for the osp invariant R ˆ operator and demonstrate the equivalence of the previous approach to the new one in the general case of the R ˆ operator invariant under the action of the osp (n  2 m) algebra.
 Publication:

Nuclear Physics B
 Pub Date:
 April 2021
 DOI:
 10.1016/j.nuclphysb.2021.115355
 arXiv:
 arXiv:2009.08143
 Bibcode:
 2021NuPhB.96515355I
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 30 pages