Less preliminary program.

Prerequisites:

a) Algebraic geometry: Chapters 2 and 3 of Hartshonre should be sufficient.

b) Homological algebra: we are going to assume a reasonable knowledge of derived and triangulated category. Chapter 1 of Kashiwara-Shapira should be sufficient.

c) Lie algebras and algebraic groups. This is going to be reminded but a prior familiarity with the basics of the subject will be very useful.

Problems on highest weight categories.

**Lecture notes for Friday, Saturday and Sunday lectures -- and a bit more**:

Notes on reductive algebraic groups.

Notes on sheaves.

Notes on category O.

Notes on rational representations in positive characteristic.

Notes on Hecke algebras and Kazhdan-Lusztig bases.

Notes on affine Weyl groups (not covered in lectures).

Notes on reductive groups, category O, and Hecke algebras
with proofs.