Andrea Appel "The R-matrix of the affine Yangian"

The theory of Yangians was introduced by Drinfeld in the 1980s as a systematic approach to solving the Yang-Baxter equation: every irreducible finite-dimensional representation is proved to be equipped with a rational R-matrix obtained by normalising the action of the universal R-matrix. Drinfeld’s proof of the existence of the universal R-matrix for Yangians of finite type was non-constructive and cohomological in nature. In this talk, I will present an alternative, explicit, and more general construction, which extends to the case of Yangians of affine type and their representations in category O. This is based on a joint work with S. Gautam and C. Wendlandt.