Math 711 Fall 2011
Introduction to geometric representation theory

Lectures: TTh 10:00-11:30, 3866 East Hall

Instructor: Thomas Lam, 2834 East Hall,

Office Hours: By appointment.

[CG] Representation theory and complex geometry. Chriss and Ginzburg
[HTT] D-modules, perverse sheaves, and representation theory. Hotta, Takeuchi, Tanisaki
[Hum] Introduction to Lie algebras and Representation Theory. Humphreys
[Gai] Lecture notes on Geometric Representation Theory. Gaitsgory
[Bor] Linear algebraic groups. Borel
[Har] Algebraic Geometry. Hartshorne
[FH] Representation Theory. Fulton and Harris
[Hum2] Representations of Semisimple Lie Algebras in the BGG Category O. Humphreys


  1. Review of complex semisimple Lie algebras
  2. Borel subgroups, flag varieties, Bruhat decomposition
  3. Borel-Weil Theorem. Maybe Bott's extension.
  4. Universal enveloping algebra, Verma modules, Category O. Statement of Kazhdan-Lusztig conjecture.
  5. Harish-Chandra isomorphism. Chevalley restriction theorem.
  6. Nilpotent cone. Springer resolution. Kostant's theorem on polynomial rings.
  7. D-modules.
  8. D-modules on flag varieties. Beilinson-Bernstein localization.