Cohomological Induction and Unitary Representations: 45 (Princeton Mathematical Series, 45) - Hardcover

Knapp, Anthony W.; Vogan, David A.

Hardcover

ISBN 10: 0691037566 ISBN 13: 9780691037561

Verlag: Princeton University Press, 1995

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Anthony W. Knapp is Professor of Mathematics at the State University of New York at Stony Brook. David A. Vogan, Jr., is Professor of Mathematics at the Massachusetts Institute of Technology.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 1995
• Sprache: Englisch
• ISBN 10: 0691037566
• ISBN 13: 9780691037561
• Einband: Tapa dura
• Anzahl der Seiten: 968
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar