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Princeton Mathematical Series #45: Cohomological Induction and Unitary Representations (PMS-45)

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Princeton Mathematical Series #45: Cohomological Induction and Unitary Representations (PMS-45) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Description:

Includes bibliographical references (p. 919-932) and indexes.

Table of Contents

Preface
Prerequisites by Chapter
Standard Notation
Introduction
IHecke Algebras
IIThe Category C(g, K)
IIIDuality Theorem
IVReductive Pairs
VCohomological Induction
VISignature Theorem
VIITranslation Functors
VIIIIrreducibility Theorem
IXUnitarizability Theorem
XMinimal K Types
XITransfer Theorem
XIIEpilog: Weakly Unipotent Representations
App. A. Miscellaneous Algebra
App. B. Distributions on Manifolds
App. C. Elementary Homological Algebra
App. D. Spectral Sequences
Notes
References
Index of Notation
Index

Product Details

ISBN:
9780691037561
With:
Vogan, David A.
Author:
Vogan, David A.
With:
Vogan, David A., Jr. JR JR JR
With:
Vogan, David A., Jr. JR
With:
Vogan, David A., Jr.
Author:
, Anthony W.
Author:
Knapp
Author:
Knapp, Anthony W.
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
Advanced
Subject:
Algebra - Linear
Subject:
Representations of groups
Subject:
Homology theory
Subject:
Harmonic analysis
Subject:
Semisimple Lie groups.
Subject:
Mathematics
Subject:
Physics
Subject:
Algebra - Abstract
Subject:
Mathematics-Linear Algebra
Copyright:
Series:
Princeton Mathematical Series
Series Volume:
TN-21945
Publication Date:
May 1995
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
968
Dimensions:
9 x 6 in 54 oz

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Related Subjects

Education » Writing
Science and Mathematics » Mathematics » Algebra » Linear Algebra
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Princeton Mathematical Series #45: Cohomological Induction and Unitary Representations (PMS-45) New Hardcover
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Product details 968 pages Princeton University Press - English 9780691037561 Reviews:
"Synopsis" by , 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.

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