Cohomological induction and unitary representations
By: Knapp, Anthony W.
Contributor(s): Vogan, David A.
Series: Princeton Mathematical series. / edited by Luis A. Caffarelli, John N. Mather and Elias M. Stein ; 45.Publisher: Princeton Princeton University Press 1995Description: xvii, 948p.ISBN: 9780691037561.Subject(s): Semisimple Lie groups | Representations of groups | Homology theory | Harmonic analysisDDC classification: 512.55 | K727c 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. 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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PK Kelkar Library, IIT Kanpur | General Stacks | 512.55 K727c (Browse shelf) | Available | A185709 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
| 512.55 K113i3 Infinite dimensional lie algebras | 512.55 K115PE REARRANGEMENTS OF SERIES IN BANACH SPACES | 512.55 K148A ALGEBRAIC TOPOLOGY VIA DIFFERENTIAL GEOMETRY | 512.55 K727c Cohomological induction and unitary representations | 512.55 K727L LIE GROUPS BEYOND AN INTRODUCTION | 512.55 K727L2 LIE GROUPS BEYOND AN INTRODUCTION | 512.55 K727r REPRESENTATION THEORY OF SEMI-SIMPLE GROUPS |
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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