## Spring 2024: *Geometric Representation Theory I *

Logistics

OH: Mon. 4pm-5pm; Thu. 3pm-4pm. Location: my office

** Lecture 1: Semisimple Lie Algebras ** Notes

** Lecture 2: Verma Modules and Category O ** Notes

** Lecture 3: Algebraic Groups ** Notes

** Lecture 4: Blocks and Harish-Chandra Isomorphism ** Notes

** Lecture 5: Proof of Harish-Chandra Isomorphism ** Notes

** Lecture 6: More on Spec(Z(g)); Finite Length ** Notes

** Lecture 7: Verma--BGG theorem ** Notes

** Lecture 8: Kazhdan--Lusztig conjecture; Duality; Projectives ** Notes

** Lecture 9: BGG reciprocity; Translation functors ** Notes

** Lecture 10: D-modules ** Notes

** Lecture 11: Six operations ** Notes

** Lecture 12: Localization Theorem ** Notes

** Lecture 13: Proof of Localization Theorem I ** Notes

** Lecture 14: Proof of Localization Theorem II; Storytelling ** Notes

** Homework solutions by 戴文晗(WenHan Dai): **

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6