Drinfeld proved that the Yangian Yg of a complex semisimple Lie

algebra g gives rise to solutions of the quantum Yang-Baxter equations

on irreducible, finite-dimensional representations of Yg, which are

rational in the spectral parameter. This result was recently extended

by Maulik-Okounkov for Kac-Moody algebras corresponding to

quivers, and representations arising from geometry.

Surprisingly perhaps, this rationality ceases to hold if one considers

arbitrary finite-dimensional representations of Yg, at least if one

requires such solutions to be natural with respect to the representation

and compatible with tensor products.

I will explain how one can instead produce meromorphic solutions

of the QYBE on all finite-dimensional representations by resumming

Drinfeld’s universal R-matrix R(s) of Yg. The construction hinges on

resumming the abelian part of R(s), and on realizing its lower triangular

part as a twist conjugating the standard coproduct of Yg to its deformed

Drinfeld coproduct.

This is joint work with Sachin Gautam and Curtis Wendlandt, and

is based on arXiv:1907.03525