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Cohomological induction and unitary representations / Anthony W. Knapp and David A. Vogan, Jr.

By: Knapp, Anthony W.
Contributor(s): Vogan, David A, 1954-.
Material type: materialTypeLabelBookSeries: Princeton mathematical series ; no. 45.Publisher: Princeton, N.J. : Princeton University Press, 1995Description: xvii, 948 p. : ill. ; 24 cm.ISBN: 0691037566 (acidfree).Subject(s): Semisimple Lie groups | Grupos de Lie semisimples | Representations of groups | Homology theory | Harmonic analysis
Contents:
I. Hecke Algebras -- II. The Category C(g, K) -- III. Duality Theorem -- IV. Reductive Pairs -- V. Cohomological Induction -- VI. Signature Theorem -- VII. Translation Functors -- VIII. Irreducibility Theorem -- IX. Unitarizability Theorem -- X. Minimal K Types -- XI. Transfer Theorem -- XII. Epilog: Weakly Unipotent Representations -- App. A. Miscellaneous Algebra -- App. B. Distributions on Manifolds -- App. C. Elementary Homological Algebra -- App. D. Spectral Sequences.
Summary: 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.Summary: Later a parallel construction using complex analysis and its associated cohomology 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.Summary: . The book, which is accessible to students beyond their 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.
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Includes bibliographical references (p. 919-932) and indexes.

I. Hecke Algebras -- II. The Category C(g, K) -- III. Duality Theorem -- IV. Reductive Pairs -- V. Cohomological Induction -- VI. Signature Theorem -- VII. Translation Functors -- VIII. Irreducibility Theorem -- IX. Unitarizability Theorem -- X. Minimal K Types -- XI. Transfer Theorem -- XII. Epilog: Weakly Unipotent Representations -- App. A. Miscellaneous Algebra -- App. B. Distributions on Manifolds -- App. C. Elementary Homological Algebra -- App. D. Spectral Sequences.

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 cohomology 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 their 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.

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