David A. Vogan's Books

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

By: Anthony W. Knapp,David A. Vogan Jr.

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

By: Anthony W. Knapp,David A. Vogan Jr.

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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968

Publisher

Princeton University Press

Published Date

ISBN 10

1400883938

ISBN 13

9781400883936

Representation Theory and Complex Analysis

Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004

By: Michael Cowling,Edward Frenkel,Masaki Kashiwara,Alain Valette,David A. Vogan,Nolan R. Wallach

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Representation Theory and Complex Analysis

Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004

By: Michael Cowling,Edward Frenkel,Masaki Kashiwara,Alain Valette,David A. Vogan,Nolan R. Wallach

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.

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Page Count

400

Publisher

Springer

Published Date

ISBN 10

3540768920

ISBN 13

9783540768920

Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118

By: David A. Vogan Jr.

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Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118

By: David A. Vogan Jr.

This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

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319

Publisher

Princeton University Press

Published Date

ISBN 10

1400882389

ISBN 13

9781400882380

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

By: Anthony W. Knapp,David A. Vogan Jr.

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

By: Anthony W. Knapp,David A. Vogan Jr.

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Solve jigsaw puzzle

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Page Count

968

Publisher

Princeton University Press

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ISBN 10

1400883938

ISBN 13

9781400883936

Book's by David A. Vogan

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

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

Representation Theory and Complex Analysis

Representation Theory and Complex Analysis

Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118

Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118

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

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

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