Rational Lax matrices from antidominantly shifted extended Yangians: BCD types

TL;DR

This paper constructs rational Lax matrices for classical Lie algebras using shifted Yangians, confirming recent physics conjectures and providing explicit algebraic realizations.

Contribution

It introduces a new family of rational Lax matrices for classical types via the RTT realization of shifted Yangians, extending previous work and confirming conjectures.

Findings

Constructed rational Lax matrices for BCD types

Provided RTT realization of shifted Yangians

Confirmed conjectures from physics literature

Abstract

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 the divisors on the projective line with coefficients being dominant integral coweights of associated Lie algebras. To this end, we provide the RTT realization of the antidominantly shifted extended Drinfeld Yangians of $\mathfrak{so}_{2r}, \mathfrak{sp}_{2r}, \mathfrak{so}_{2r+1}$, and of their coproduct homomorphisms. This establishes some of the recent conjectures in the physics literature by Costello-Gaiotto-Yagi (arXiv:2103.01835) in the classical types.