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Contents
§1.9. Harish-Chandra Homomorphism 25
§1.10. Harish-Chandra's Theorem 26
§1.11. Category O is Artinian 28
§1.12. Subcategories Ox 30
§1.13. Blocks 30
§1.14. Formal Characters of Finite Dimensional Modules 32
§1.15. Formal Characters of Modules in O 33
§1.16. Formal Characters of Verma Modules 34
Notes 35
Chapter 2. Characters of Finite Dimensional Modules 37
§2.1. Summary of Prerequisites 37
§2.2. Formal Characters Revisited 38
§2.3. The Functions p and q 38
§2.4. Formulas of Weyl and Kostant 40
§2.5. Dimension Formula 42
§2.6. Maximal Submodule of M(A), A G A+ 43
§2.7. Related Topics 45
Notes 46
Chapter 3. Category O: Methods 47
§3.1. Horn and Ext 47
§3.2. Duality in O 49
§3.3. Duals of Highest Weight Modules 51
§3.4. The Reflection Group W[X] 52
§3.5. Dominant and Antidominant Weights 54
§3.6. Tensoring Verma Modules with Finite Dimensional Modules 56
§3.7. Standard Filtrations 58
§3.8. Projectives in O 60
§3.9. Indecomposable Projectives 62
§3.10. Standard Filtrations of Projectives 64
§3.11. BGG Reciprocity 65
§3.12. Example: sI(2,C) 66
§3.13. Projective Generators and Finite Dimensional Algebras 68
§3.14. Contravariant Forms 68
§3.15. Universal Construction 70
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