Real Reductive Groups II
Published on 6. August 1992
453 pages
978-0-08-087452-4 (ISBN)
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Real Reductive Groups II
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Nolan R. Wallach
Real Reductive Groups: No. 2
Book
01/1992
Academic Press
€108.94
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Content
- Front Cover
- Real Reductive Groups II
- Copyright Page
- Contents
- Preface
- Introduction
- Chapter 10. Intertwining Operators
- Introduction
- 10.1. The intertwining operators
- 10.2. The proof of Theorem 10.1.5
- 10.3. Limit formulas
- 10.4. A generalization of L. Cohn's determinant formula
- 10.5. The Harish-Chandra µ-function
- 10.6. Notes and further results
- 10.A. Appendices to Chapter 10
- 10.A.l. Some constructions related to finite dimensional representations
- 10.A.2. Some results related to Sterling's formula
- 10.A.3. Miscellaneous results
- Chapter 11. Completions of Admissible (g, K)-Modules
- Introduction
- 11.1. Some results on Weyl group invariants
- 11.2. A lemma of Kostant
- 11.3. Representations with small K-types
- 11.4. The automatic continuity theorem
- 11.5. Completions of (g, K)-modules
- 11.6. Analysis of completions of (g, K)-modules
- 11.7. The proof of the main theorem
- 11.8. The action of f(G) on admissible representations
- 11.9. Poisson integral representations
- 11.10. Notes and further results
- 1l.A. Appendices to Chapter 11
- 11.A.l. Some results on the action of a compact group on a symmetric algebra
- 11.A.2. Small K-types
- 11.A.3. Some results on Verma modules
- 11.A.4. Some functional analysis
- Chapter 12. The Theory of the Leading Term
- Introduction
- 12.1. Characters of principal series representations
- 12.2. The modules VQ|P,s,iv
- 12.3. The leading term
- 12.4. The dependence of the leading term on parameters
- 12.5. The leading term and intertwining operators
- 12.6. The main inequality
- 12.7. Wave packets
- 12.8. The Harish-Chandra transform of a wave packet
- 12.9. Notes
- 12.A. Appendices to Chapter 12
- 12.A.1. Traces of certain kernel operators
- 12.A.2. Some inequalities
- 12.A.3. The topology of induced representations
- Chapter 13. The Harish-Chandra Plancherel Theorem
- Introduction
- 13.1. The Eisenstein integral
- 13.2. The leading terms of Eisenstein integrals
- 13.3. Wave packets of Eisenstein integrals
- 13.4. The Harish-Chandra Plancherel theorem
- 13.5. The calculation of µ(?, ?) for the fundamental series
- 13.6. The intertwining algebra of Ip,s,iv and the irreducibility of the fundamental series
- 13.7. Groups with one conjugacy class of Cartan subgroup
- 13.8. The Plancherel theorem for L2(G/K)
- 13.9. Notes and further results
- Chapter 14. Abstract Representation Theory
- Introduction
- 14.1. The basic theory of C* algebras
- 14.2. The C* algebra of a locally compact group
- 14.3. Quotients of C* algebras
- 14.4. Density theorems
- 14.5. Representations of C* algebras and positive functionals
- 14.6. The topology on the unitary dual of a C* algebra
- 14.7. The topology on the unitary dual of a locally compact group
- 14.8. Direct integrals and Von Neumann algebras
- 14.9. Direct integrals of representations of C* algebras and locally compact groups
- 14.10. Decompositions of representations of CCR C* algebras and locally compact groups
- 14.11. The Plancherel formula for CCR locally compact, unimodular groups
- 14.12. The Plancherel formula for real reductive groups
- 14.13. Notes and further results
- 14.A. Some functional analysis
- Chapter 15. The Whittaker Plancherel Theorem
- Introduction
- 15.1. The support of certain induced representations
- 15.2. Some asymptotic expansions and estimates
- 15.3. The Schwartz space for L2(N \ G
- ?)
- 15.4. The holomorphic continuation of the Jacquet integral
- 15.5. First steps for the holomorphic continuation
- 15.6. The completion of the proof of the holomorphic continuation
- 15.7. Cusp forms revisited
- 15.8. The first steps for the Plancherel theorem for generic ?
- 15.9. The Plancherel theorem for L2N0 \ G
- ?)
- 15.10. Some examples of the Plancherel theorem for generic ?
- 15.11. Notes and further results
- 15.A. Appendix to Chapter 15
- Bibliography
- Index
- Pure and Applied Mathematics
