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