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|a 1175635984
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|a UAMI
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|a Knapp, Anthony W.,
|e author.
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|a Cohomological induction and unitary representations /
|c Anthony W. Knapp and David A. Vogan, Jr.
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|a Princeton, N.J. :
|b Princeton University Press,
|c 1995.
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| 300 |
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|a 1 online resource (xvii, 948 pages)
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a data file
|2 rda
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|a Princeton mathematical series ;
|v 45
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|a Includes bibliographical references and indexes.
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|a Online resource; title from PDF title page (EBSCO, viewed May 5, 2016).
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|6 880-01
|a 5. Abstract Construction6. Hecke Algebras for Pairs (g, K); II. THE CATEGORY C(g, K); 1. Functors P and I; 2. Properties of P and I; 3. Constructions within C(g, K); 4. Special Properties of P and I in Examples; 5. Mackey Isomorphisms; 6. Derived Functors of P and I; 7. Standard Resolutions; 8. Koszul Resolution as a Complex; 9. Reduction of Exactness for the Koszul Resolution; 10. Exactness in the Abelian Case; III. DUALITY THEOREM; 1. Easy Duality; 2. Statement of Hard Duality; 3. Complexes for Computing Pj and I^j; 4. Hard Duality as a K Isomorphism; 5. Proof of g Equivariance in Case (i).
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|a 6. Motivation for g Equivariance in Case (ii)7. Proof of g Equivariance in Case (ii); 8. Proof of Hard Duality in the General Case; IV. REDUCTIVE PAIRS; 1. Review of Cartan-Weyl Theory; 2. Cartan-Weyl Theory for Disconnected Groups; 3. Reductive Groups and Reductive Pairs; 4. Cartan Subpairs; 5. Finite-Dimensional Representations; 6. Parabolic Subpairs; 7. Harish-Chandra Isomorphism; 8. Infinitesimal Character; 9. Kostant's Theorem; 10. Casselman-Osborne Theorem; 11. Algebraic Analog of Bott-Borel-Weil Theorem; V. COHOMOLOGICAL INDUCTION; 1. Setting; 2. Effect on Infinitesimal Character.
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|a 3. Preliminary Lemmas4. Upper Bound on Multiplicities of K Types; 5. An Euler-Poincaré Principle for K Types; 6. Bottom-Layer Map; 7. Vanishing Theorem; 8. Fundamental Spectral Sequences; 9. Spectral Sequences for Analysis of K Types; 10. Hochschild-Serre Spectral Sequences; 11. Composite P Functors and I Functors; VI. SIGNATURE THEOREM; 1. Setting; 2. Hermitian Dual and Signature; 3. Hermitian Duality Relative to P and I; 4. Statement of Signature Theorem; 5. Comparison of Shapovalov Forms on K and G; 6. Preservation of Positivity from L)"K to K.
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|a 7. Signature Theorem for K Badly DisconnectedVII. TRANSLATION FUNCTORS; 1. Motivation and Examples; 2. Generalized Infinitesimal Character; 3. Chevalley's Structure Theorem for Z(g); 4. Z(l) Finiteness of u Homology and Cohomology; 5. Invariants in the Symmetric Algebra; 6 . Kostant's Theory of Harmonics; 7. Dixmier-Duflo Theorem; 8 . Translation Functors; 9. Integral Dominance; 10. Overview of Preservation of Irreducibility; 11. Details of Irreducibility; 12. Nonvanishing of Certain Translation Functors; 13. Application to (g, K) Modules with K Connected.
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|a JSTOR
|b Books at JSTOR All Purchased
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|a JSTOR
|b Books at JSTOR Evidence Based Acquisitions
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|a JSTOR
|b Books at JSTOR Demand Driven Acquisitions (DDA)
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| 650 |
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|a Semisimple Lie groups.
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| 650 |
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|a Representations of groups.
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| 650 |
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|a Homology theory.
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| 650 |
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|a Harmonic analysis.
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|a Fourier Analysis
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| 650 |
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|a Groupes de Lie semi-simples.
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| 650 |
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|a Représentations de groupes.
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| 650 |
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|a Homologie.
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| 650 |
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|a Analyse harmonique.
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| 650 |
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|a MATHEMATICS
|x Algebra
|x Intermediate.
|2 bisacsh
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| 650 |
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|a MATHEMATICS
|x Algebra
|x Abstract.
|2 bisacsh
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| 650 |
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|a Harmonic analysis.
|2 fast
|0 (OCoLC)fst00951490
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| 650 |
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|a Homology theory.
|2 fast
|0 (OCoLC)fst00959720
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| 650 |
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|a Representations of groups.
|2 fast
|0 (OCoLC)fst01094938
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| 650 |
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|a Semisimple Lie groups.
|2 fast
|0 (OCoLC)fst01112374
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| 700 |
1 |
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|a Vogan, David A.,
|d 1954-
|e author.
|
| 776 |
0 |
8 |
|i Print version:
|a Knapp, Anthony W.
|t Cohomological Induction and Unitary Representations (PMS-45).
|d Princeton : Princeton University Press, ©2016
|z 9780691037561
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| 830 |
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|a Princeton mathematical series ;
|v 45.
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| 856 |
4 |
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|u https://jstor.uam.elogim.com/stable/10.2307/j.ctt1bpm9qm
|z Texto completo
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| 880 |
0 |
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|6 505-01/(S
|a Cover; Title; Copyright; Dedication; CONTENTS; Preface; Prerequisites by Chapter; Standard Notation; INTRODUCTION; 1. Origins of Algebraic Representation Theory; 2. Early Constructions of Representations; 3. Sections of Homogeneous Vector Bundles; 4. Zuckerman Functors; 5. Cohomological Induction; 6. Hecke Algebra and the Definition of π; 7. Positivity and the Good Range; 8. One-Dimensional Z and the Fair Range; 9. Transfer Theorem; I. HECKE ALGEBRAS; 1. Distributions on Lie Groups; 2. Hecke Algebras for Compact Lie Groups; 3. Approximate Identities; 4. Hecke Algebras in the Group Case.
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|a Internet Archive
|b INAR
|n cohomologicalind0000knap
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| 938 |
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|a Askews and Holts Library Services
|b ASKH
|n AH31319097
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| 938 |
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|a ProQuest Ebook Central
|b EBLB
|n EBL4510792
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| 938 |
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|a EBSCOhost
|b EBSC
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