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Contents
§6.6. Application: Bott's Theorem 115
§6.7. Squares 116
§6.8. Maps in a BGG Resolution 118
§6.9. Homological Dimension 120
§6.10. Higher Ext Groups 122
§6.11. Vanishing Criteria for
Extn
123
§6.12. Computation of Extg,(M(/x),
M(A)V)
124
§6.13. Ext Criterion for Standard Filtrations 125
§6.14. Characters in Terms of Extp 126
§6.15. Comparison of Ext£ and Lie Algebra Cohomology 127
Notes 128
Chapter 7. Translation Functors 129
§7.1. Translation Functors 130
§7.2. Adjoint Functor Property 131
§7.3. Weyl Group Geometry 132
§7.4. Nonintegral Weights 134
§7.5. Key Lemma 135
§7.6. Translation Functors and Verma Modules 137
§7.7. Translation Functors and Simple Modules 138
§7.8. Application: Category Equivalences 138
§7.9. Translation to Upper Closures 140
§7.10. Character Formulas 142
§7.11. Translation Functors and Projective Modules 143
§7.12. Translation from a Facet Closure 144
§7.13. Example 145
§7.14. Translation from a Wall 146
§7.15. Wall-Crossing Functors 148
§7.16. Self-Dual Projectives 149
Notes 152
Chapter 8. Kazhdan-Lusztig Theory 153
§8.1. The Multiplicity Problem for Verma Modules 154
§8.2. Hecke Algebras and Kazhdan-Lusztig Polynomials 156
§8.3. Examples 157
§8.4. Kazhdan-Lusztig Conjecture 159
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