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Cohomological Induction and Unitary Representations (PMS-45), Volume 45 : Princeton Mathematical Series - Anthony W. Knapp

Cohomological Induction and Unitary Representations (PMS-45), Volume 45

Princeton Mathematical Series

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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.

Winner of the 1996 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers "This book is a thorough and excellent presentation of the 'cohomological' approach to the construction and classification of irreducible representations of semisimple real Lie groups..."--Zentralblatt f?r Mathematik

Prerequisites by Chapter
Standard Notation
Hecke Algebras
The Category C(g, K)
Duality Theorem
Reductive Pairs
Cohomological Induction
Signature Theorem
Translation Functors
Irreducibility Theorem
Unitarizability Theorem
Minimal K Types
Transfer Theorem
Epilog: Weakly Unipotent Representations
Miscellaneous Algebra
Distributions on Manifolds
Elementary Homological Algebra
Spectral Sequences
Index of Notation
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691037561
ISBN-10: 0691037566
Series: Princeton Mathematical Series
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 968
Published: 1st May 1995
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 5.7
Weight (kg): 1.47