Overview of Springer theory (1/5)

algebraic geometrycombinatoricsrepresentation theory

Audience: researchers in the discipline

IBS-CGP and PMI Lecture Series

Series comments: Since the groundbreaking paper of Springer, Springer theory becomes one of the most fundamental topics in geometric representation theory. This is originally developed in order to study the representation theory of Weyl groups. However, it is now known to be closely related to the representation theory of Hecke algebras, finite groups of Lie type, Lie algebras, and their affine analogues. Furthermore, this became a starting point of various areas in geometric representation theory such as character sheaves, symplectic resolutions, parity sheaves. On the other hand, it also has a strong connection with algebraic combinatorics which makes the theory more fruitful. The goal of this talk is to give a brief introduction of Springer theory with some small examples, instead of delving into technical details and long proofs.