Introduction to Categorical Representation Theory

Oded Yacobi – 7 June 2017

In recent years interactions between representation theory and category theory have led to exciting discoveries and solutions of several important problems. In this talk I will give an overview of some of these developments. I will start with the origin story, namely Chuang and Rouquier's notion of a categorical sl(2)-representation and its applications to modular representation theory of the symmetric group. Then I will discuss categorical g-representations, for any semi simple Lie algebra g, and the appearance of these structures in some of my own work related to Schubert varieties in the affine Grassmannian. If there is time, I would like to also discuss some open problems in this area that I think will require tools from higher category theory.