Cohomological Induction and Unitary Representations (PMS-45), Volume 45 / / David A. Vogan, Anthony W. Knapp.

• Superior document: Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
• VerfasserIn: Knapp, Anthony W.,; Vogan, David A.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1995
• Year of Publication: 2016
• Language: English
• Series: Princeton Mathematical Series ; 45
• Physical Description: 1 online resource (968 p.)
• Other title: Frontmatter --; CONTENTS --; PREFACE --; PREREQUISITES BY CHAPTER --; STANDARD NOTATION --; INTRODUCTION --; CHAPTER I. HECKE ALGEBRAS --; CHAPTER II. THE CATEGORY C(g, K) --; CHAPTER III. DUALITY THEOREM --; CHAPTER IV. REDUCTIVE PAIRS --; CHAPTER V. COHOMOLOGICAL INDUCTION --; CHAPTER VI. SIGNATURE THEOREM --; CHAPTER VII. TRANSLATION FUNCTORS --; CHAPTER VIII. IRREDUCIBILITY THEOREM --; CHAPTER IX. UNITARIZABILITY THEOREM --; CHAPTER X. MINIMAL K TYPES --; CHAPTER XI. TRANSFER THEOREM --; CHAPTER XII. EPILOG: WEAKLY UNIPOTENT REPRESENTATIONS --; APPENDIX A. MISCELLANEOUS ALGEBRA --; APPENDIX B. DISTRIBUTIONS ON MANIFOLDS --; APPENDIX C. ELEMENTARY HOMOLOGICAL ALGEBRA --; APPENDIX D. SPECTRAL SEQUENCES --; NOTES --; REFERENCES --; INDEX OF NOTATION --; INDEX
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400883936; 9783110501063; 9783110442496
• DOI: 10.1515/9781400883936
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: David A. Vogan, Anthony W. Knapp.

This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.