Chapter VI. Holomorphic Discrete Series

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface to the Princeton Landmarks in Mathematics Edition xiii
4. Preface xv
5. Acknowledgments xix
6. Chapter I. Scope of the Theory 1
7. Chapter II. Representations of SU(2), SL(2, ℝ) and SL(2, ℂ) 28
8. Chapter III. C^∞ Vectors and the Universal Enveloping Algebra 46
9. Chapter IV. Representations of Compact Lie Groups 60
10. Chapter V. Structure Theory for Noncompact Groups 113
11. Chapter VI. Holomorphic Discrete Series 150
12. Chapter VII. Induced Representations 167
13. Chapter VIII. Admissible Representations 203
14. Chapter IX. Construction of Discrete Series 281
15. Chapter X. Global Characters 333
16. Chapter XI. Introduction to Plancherel Formula 385
17. Chapter XII. Exhaustion of Discrete Series 426
18. Chapter XIII. Plancherel Formula 482
19. Chapter XIV. Irreducible Tempered Representations 515
20. Chapter XV. Minimal K Types 626
21. Chapter XVI. Unitary Representations 650
22. Appendix A. Elementary Theory of Lie Groups 667
23. Appendix B. Regular Singular Points of Partial Differential Equations 685
24. Appendix C. Roots and Restricted Roots for Classical Groups 713
25. Notes 719
26. References 747
27. Index of Notation 763
28. Index 767