Springer fibers in representation theory
Student No.:50
Time:Mon/Wed 10:10-12:00, 2016-11-28~ 2016-12-21 (No classes on public holidays)
Instructor:Peng Shan  [CNRS/Université Paris Sud]
Place:Conference room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2016-11-28
Ending Date:2016-12-21





Springer fibers are an important family of varieties used in geometric representation theory. The goal of this course is to give an introduction to these varieties, their geometric structures and explain some relationships between their cohomology and the center of some representation categories of Lie algebras. We plan to cover the following topics:

1. Definition and basic properties

2. Cohomology of Springer fibers and Springer representation

3. De Concini--Procesi’s description as the function ring of a T-fixed point scheme in the closure of a nilpotent orbit in type A.

4. Isomorphism with the center of parabolic category O in type A.




Basics in representation of Lie algebras and algebraic topology would be helpful but not obligatory.



Brundan, Jonathan Centers of degenerate cyclotomic Hecke algebras and parabolic category 𝒪. Represent. Theory 12 (2008), 236–259.

De Concini, Corrado; Procesi, Claudio
Symmetric functions, conjugacy classes and the flag variety.
Invent. Math. 64 (1981), no. 2, 203–219.

Stroppel, Catharina Parabolic category 𝒪, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology. Compos. Math. 145 (2009), no. 4, 954–992.

Zhiwei Yun Lectures on Springer theories and orbital integrals arXiv:1602.01451