Mathematics > Representation Theory
[Submitted on 29 Apr 2021 (v1), last revised 9 Mar 2022 (this version, v3)]
Title:Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
View PDFAbstract: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.
Submission history
From: Alexander Tsymbaliuk [view email][v1] Thu, 29 Apr 2021 17:34:17 UTC (65 KB)
[v2] Mon, 12 Jul 2021 17:39:00 UTC (68 KB)
[v3] Wed, 9 Mar 2022 14:12:36 UTC (67 KB)
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