Second-order evaluations of orthogonal and symplectic Yangians

Abstract

Orthogonal or symplectic Yangians are defined by the Yang–Baxter RLL relation involving the fundamental R-matrix with the corresponding so(n) or sp(2m) symmetry. We investigate the second-order solution conditions, where the expansion of L(u) in u⁻¹is truncated at the second power, and we derive the relations for the two nontrivial terms in L(u).