Orthogonal and symplectic Yangians and Yang-Baxter R-operators

TL;DR

This paper studies Yang-Baxter R operators symmetric to orthogonal and symplectic algebras, deriving explicit forms and exploring their associated L operators, including truncated expansions and fusion processes, revealing new algebraic conditions and representations.

Contribution

It provides explicit forms of spinorial and metaplectic R operators and analyzes truncated L operators with orthogonal and symplectic symmetries, introducing fusion techniques for these operators.

Findings

Explicit forms for spinorial and metaplectic R operators.

Conditions for truncated L operators in orthogonal and symplectic cases.

Fusion methods reproducing second order L operators.

Abstract

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalised L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.