R-matrices of affine Yangians

Abstract: Yangians are certain remarkable Hopf algebras, associated to finite-dimensional simple Lie algebras, introduced by Drinfeld in the 1980's. Drinfeld proved, in a non-constructive manner, that each Yangian comes equipped with a formal solution to the famous Yang-Baxter equation, known as Drinfeld's universal R-matrix.

In this talk, I will present a very concrete method to construct Drinfeld's universal R-matrix using additive difference equations. I will explain how our method generalizes to other situations where no analogue of Drinfeld's result is known, such as Yangians associated to affine Kac-Moody algebras. I will highlight the significant differences between the finite and affine situations, and the new challenges present in the latter.

This talk is based on earlier works joint with Valerio Toledano Laredo and Curtis Wendlandt, and a recent one in collaboration with Andrea Appel and Curtis Wendlandt.

mathematical physicsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Comments: Hybrid delivery (in person on University of Saskatchewan campus and via Zoom).

PIMS Geometry / Algebra / Physics (GAP) Seminar