Unitary Representations Of Real Reductive Groups

Author : Nolan R. Wallach
Publisher : Academic Press
ISBN 13 : 0080874517
Total Pages : 439 pages
Book Rating : 4.17/5 ( download)

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Download or read book Real Reductive Groups I written by Nolan R. Wallach and published by Academic Press. This book was released on 1988-03-01 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

Author : David A. Vogan
Publisher : Princeton University Press
ISBN 13 : 9780691084824
Total Pages : 324 pages
Book Rating : 4.23/5 ( download)

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Download or read book Unitary Representations of Reductive Lie Groups written by David A. Vogan and published by Princeton University Press. This book was released on 1987-10-21 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jeffrey Adams
Publisher :
ISBN 13 : 9782856299180
Total Pages : 174 pages
Book Rating : 4.80/5 ( download)

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Download or read book Unitary Representations of Real Reductive Groups written by Jeffrey Adams and published by . This book was released on 2020 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Anthony W. Knapp
Publisher : Princeton University Press
ISBN 13 : 1400883938
Total Pages : 968 pages
Book Rating : 4.36/5 ( download)

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Download or read book Cohomological Induction and Unitary Representations (PMS-45), Volume 45 written by Anthony W. Knapp and published by Princeton University Press. This book was released on 2016-06-02 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author :
Publisher : Academic Press
ISBN 13 : 0080874525
Total Pages : 475 pages
Book Rating : 4.24/5 ( download)

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Download or read book Real Reductive Groups II written by and published by Academic Press. This book was released on 1992-08-06 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Reductive Groups II

Author : David A. Vogan
Publisher :
ISBN 13 : 9780691084817
Total Pages : 308 pages
Book Rating : 4.15/5 ( download)

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Download or read book Unitary Representations of Reductive Lie Groups written by David A. Vogan and published by . This book was released on 1987 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Nolan R. Wallach
Publisher : Academic Press
ISBN 13 : 9780127329604
Total Pages : 412 pages
Book Rating : 4.09/5 ( download)

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Download or read book Real Reductive Groups I written by Nolan R. Wallach and published by Academic Press. This book was released on 1988-03-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

Author : David A. Vogan
Publisher : Birkhauser
ISBN 13 :
Total Pages : 782 pages
Book Rating : 4.39/5 ( download)

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Download or read book Representations of Real Reductive Lie Groups written by David A. Vogan and published by Birkhauser. This book was released on 1981 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Eng-chye Tan
Publisher : World Scientific
ISBN 13 : 981238779X
Total Pages : 426 pages
Book Rating : 4.90/5 ( download)

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Download or read book Representations of Real and P-adic Groups written by Eng-chye Tan and published by World Scientific. This book was released on 2004 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on ?Representation Theory of Lie Groups? from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadi? from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pand?i? from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.

Author : J. Adams
Publisher : Springer Science & Business Media
ISBN 13 : 146120383X
Total Pages : 331 pages
Book Rating : 4.34/5 ( download)

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Download or read book The Langlands Classification and Irreducible Characters for Real Reductive Groups written by J. Adams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.