Sep 29 | Basic definitions (1.1) Basic operations (1.2) |
Week 1 | |
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Oct 2 | Representations of sl2 (1.3) Roadmap (1.4) |
Oct 4 | Enveloping algebras, definition (2.1) PBW basis (2.2) |
Oct 6 | Induction (2.3) Verma modules for sl2 (3.1) |
Week 2 | |
Oct 9 |
Spherical harmonics (3.2) Semisimple Lie algebras (4.1) Classical series (4.2) |
Oct 11 |
Roots and weights (4.3) Root systems (4.4) |
Oct 13 | 4.4 continued |
Week 3 | |
Oct 16 | Formal characters (4.5) Borel subalgebras (4.6) Highest weight representations (4.7) |
Oct 18 | Definition of category 𝒪 (4.8) |
Oct 20 |
Central characters (5.1) Linked weights (5.2) |
Week 4 | |
Oct 23 | Harish-Chandra's theorem (5.3) 𝒪 is artinian (5.4) Grothendieck group (5.5) |
Oct 25 | Yoneda Ext (6.1) Blocks (6.2) |
Oct 27 | Subcategories 𝒪χ (6.3) |
Week 5 | |
Oct 30 | Dominant and antidominant weights (6.4) Duality (6.5) |
Nov 1 | 6.5 continued Projective objects (7.1) |
Nov 3 | 7.1 continued |
Week 6 | |
Nov 6 | Projective covers (7.2) |
Nov 8 | Injective objects (7.3) Standard filtrations (7.4) |
Nov 10 | Holiday - no class |
Week 7 | |
Nov 13 |
Resolutions (8.1) Chevalley-Eilenberg complex (8.2) |
Nov 15 | Weights in the relative Chevalley-Eilenberg complex (8.3) |
Nov 17 | 8.3 continued |
Week 8 | |
Nov 20 | Bott's theorem (8.4) |
Nov 22 | Complements of BGG complex (8.5) Translation functors (8.6) |
Nov 24 | Holiday - no class |
Week 9 | |
Nov 27 | Kazhdan-Lusztig polynomials (9.1-9.4) |
Nov 29 | Highest weight categories (10.1) |
Dec 1 | 10.1 continued |
Week 10 | |
Dec 4 | 10.1 continued |
Dec 6 | Path algebras (10.2) |
Dec 8 | Quasi-hereditary algebras (10.3) |