Contents
XI
§8.5. Schubert Varieties and KL Polynomials 160
§8.6. Example: W of Type C3 161
§8.7. Jantzen's Multiplicity One Criterion 162
§8.8. Proof of the KL Conjecture 165
§8.9. Outline of the Proof 166
§8.10. Ext Functors and Vogan's Conjecture 168
§8.11. KLV Polynomials 169
§8.12. The Jantzen Conjecture and the KL Conjecture 171
§8.13. Weight Filtrations and Jantzen Filtrations 172
§8.14. Review of Loewy Filtrations 173
§8.15. Loewy Filtrations and KL Polynomials 174
§8.16. Some Details 177
Part II. Further Developments
Chapter 9. Parabolic Versions of Category O 181
§9.1. Standard Parabolic Subalgebras 182
§9.2. Modules for Levi Subalgebras 183
§9.3. The Category
Op
184
§9.4. Parabolic Verma Modules 186
§9.5. Example: sI(3,C) 188
§9.6. Formal Characters and Composition Factors 189
§9.7. Relative Kazhdan-Lusztig Theory 190
§9.8. Projectives and BGG Reciprocity in
Op
191
§9.9. Structure of Parabolic Verma Modules 192
§9.10. Maps between Parabolic Verma Modules 193
§9.11. Parabolic Verma Modules of Scalar Type 195
§9.12. Simplicity of Parabolic Verma Modules 196
§9.13. Jantzen's Simplicity Criterion 198
§9.14. Socles and Self-Dual Projectives 199
§9.15. Blocks of O* 200
§9.16. Analogue of the BGG Resolution 201
§9.17. Filtrations and Rigidity 203
§9.18. Special Case: Maximal Parabolic Subalgebras 204
Notes 206
Chapter 10. Projective Functors and Principal Series 207
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