Seminar: Representation Theory and Automorphic Forms

Résumé

In this talk, I will present intertwining operators from the point of view of quantum groups, that is R-matrices. R-matrices are the solutions to the Yang-Baxter equation (or braid relation), which is at the origin of the introduction of quantum groups. I will explain all of these concepts, with a focus on the case of quantum affine algebras, for which interesting things happen! If there is time, we will also see the link with mathematical physics, where R-matrices appear in the study of spectra of quantum integrable systems.