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

Yang–Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with 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 Ya...

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Bibliographic Details
Published in:Nuclear physics. B 2017-04, Vol.917 (C), p.44-85
Main Authors: Fuksa, J., Isaev, A.P., Karakhanyan, D., Kirschner, R.
Format: Article
Language:English
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Summary:Yang–Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with 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 superspinor representations and study the fusion of L-operators involving the tensor product of such representations.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2017.01.029