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

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.

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Cited by in corpus (9)

• Spinorial R operator and Algebraic Bethe Ansatz
• Yang-Baxter R-operators for osp superalgebras
• 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
• Orthogonal and symplectic Yangians - linear and quadratic evaluations
• Representations of orthogonal and symplectic Yangians