Second-order evaluations of orthogonal and symplectic Yangians

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 $u^{-1}$ is truncated at the second power, and we derive the relations for the two nontrivial terms in $L(u)$.