Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras

TL;DR

This paper explores Yang-Baxter relations and R-operators related to ortho-symplectic superalgebras, extending known algebraic structures and constructing new intertwining operators for super-spinor representations.

Contribution

It develops the theory of Yang-Baxter operators and L-operators for ortho-symplectic superalgebras, including their representations and fusion processes, advancing the understanding of superalgebra symmetries.

Findings

Constructed the vector R matrix for ortho-symplectic superalgebras.

Derived conditions for L(u) in truncated expansions.

Built R operators intertwining super-spinor representations.

Abstract

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start from the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R matrix, the L operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L(u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R operator intertwining two super-spinor representations and study the fusion of L operators involving the tensor product of such representations.