Rational Lax Matrices from Antidominantly Shifted Extended Yangians: BCD Types

Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices, polynomial in the spectral parameter, parametrized by divisors on projective line coefficients being dominant integral coweights associated Lie algebras. To this end, provide RTT realization antidominantly shifted extended Drinfeld Yangians $\mathfrak{so}_{2r}, \mathfrak{sp}_{2r}, \mathfrak{so}_{2r+1}$, and their coproduct homomorphisms. This establishes some conjectures physics literature Costello-Gaiotto-Yagi (arXiv:2103.01835) classical types.