Format:
Online Ressource (xiv, 454 pages)
Edition:
Online-Ausg.
ISBN:
9780127329611
,
0127329617
,
0127329617
Series Statement:
Pure and applied mathematics v. 132, pt. 2
Content:
Intertwining operators -- Completions of admissible (g, K)-modules -- Theory of the leading term -- Harish-Chandra Plancherel theorem -- Abstract representation theory -- Whittaker Plancherel theorem
Note:
Includes bibliographical references and indexes. - Print version record
,
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
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Introduction11.1. 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
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11.A.4. Some functional analysisChapter 12. The Theory of the Leading Term; Introduction; 12.1. Characters of principal series representations; 12.2. The modules VQ|P,σ,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
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Chapter 13. The Harish-Chandra Plancherel TheoremIntroduction; 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(ω, υ) for the fundamental series; 13.6. The intertwining algebra of Ip,σ,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
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14.1. The basic theory of C* algebras14.2. 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
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14.11. The Plancherel formula for CCR locally compact, unimodular groups
Additional Edition:
ISBN 0127329617
Additional Edition:
Erscheint auch als Druck-Ausgabe Wallach, Nolan R Real reductive groups II Boston : Academic Press, c1992
Language:
English
Keywords:
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