Category O and Soergel Theory

Graduate / Professional

Category O is one of the most important categories of representations of semisimple Lie algebras. Soergel theory provides a powerful tool of studying this category by relating it to a category of more combinatorial/ elementary nature. We cover these subjects and then proceed to a more general version of the Soergel theory that allows to prove various category equivalences between realizations of the “Hecke category,” in particular, those of interest for the geometric Langlands program. Prerequisites: structure and finite dimensional representation theory of semisimple Lie algebras over the complex numbers. For the second part of the course, familiarity with algebraic geometry, algebraic topology, and category theory (e.g. derived categories) is useful. TTh 1:05pm-2:20pm