Rational Lax matrices from antidominantly shifted extended Yangians: BCD types

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.

arXiv commentv3: 67 pages, minor corrections, details added. v2: 65 pages, minor corrections, some details added, Remark 4.37 added. v1: 64 pages, comments are welcome!

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• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Orthosymplectic Yangians
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system