Unitary Representations Of Reductive Lie Groups

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Unitary Representations of Reductive Lie Groups

Author : David A. Vogan
Publisher : Princeton University Press
ISBN 13 : 9780691084824
Total Pages : 324 pages
Book Rating : 4.0/5 (848 download)

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Book Synopsis Unitary Representations of Reductive Lie Groups by : David A. Vogan

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.

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

Author : David A. Vogan Jr.
Publisher : Princeton University Press
ISBN 13 : 1400882389
Total Pages : 319 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 by : David A. Vogan Jr.

Download or read book Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 written by David A. Vogan Jr. and published by Princeton University Press. This book was released on 2016-03-02 with total page 319 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.

Unitary Representations of Reductive Lie Groups

Author : David A. Vogan
Publisher :
ISBN 13 : 9780691084817
Total Pages : 308 pages
Book Rating : 4.0/5 (848 download)

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Book Synopsis Unitary Representations of Reductive Lie Groups by : David A. Vogan

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.

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

Author : Anthony W. Knapp
Publisher : Princeton University Press
ISBN 13 : 1400883938
Total Pages : 968 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Cohomological Induction and Unitary Representations (PMS-45), Volume 45 by : Anthony W. Knapp

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.

A Construction of Singular Unitary Representations of Reductive Lie Groups

Author : Pierluigi Möseneder Frajria
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (733 download)

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Book Synopsis A Construction of Singular Unitary Representations of Reductive Lie Groups by : Pierluigi Möseneder Frajria

Download or read book A Construction of Singular Unitary Representations of Reductive Lie Groups written by Pierluigi Möseneder Frajria and published by . This book was released on 1988 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Theory

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
ISBN 13 : 0817681922
Total Pages : 341 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Lie Theory by : Jean-Philippe Anker

Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Lie Groups, Lie Algebras, and Representations

Author : Brian C. Hall
Publisher : Springer Science & Business Media
ISBN 13 : 9780387401225
Total Pages : 376 pages
Book Rating : 4.4/5 (12 download)

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Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian C. Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.

Unitary Representation Theory for Solvable Lie Groups

Author : Jonathan Paul Brezin
Publisher : American Mathematical Soc.
ISBN 13 : 0821812793
Total Pages : 132 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Unitary Representation Theory for Solvable Lie Groups by : Jonathan Paul Brezin

Download or read book Unitary Representation Theory for Solvable Lie Groups written by Jonathan Paul Brezin and published by American Mathematical Soc.. This book was released on 1968 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic and Analytic Methods in Representation Theory

Author :
Publisher : Elsevier
ISBN 13 : 0080526950
Total Pages : 357 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Algebraic and Analytic Methods in Representation Theory by :

Download or read book Algebraic and Analytic Methods in Representation Theory written by and published by Elsevier. This book was released on 1996-09-27 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. Presents several different points of view on key topics in representation theory, from internationally known experts in the field

Representation Theory of Lie Groups

Author : Jeffrey Adams
Publisher : American Mathematical Soc.
ISBN 13 : 1470423146
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representation Theory of Lie Groups by : Jeffrey Adams

Download or read book Representation Theory of Lie Groups written by Jeffrey Adams and published by American Mathematical Soc.. This book was released on 2015-06-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant "philosophy of coadjoint orbits" for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of "localization". And Jian-Shu Li covers Howe's theory of "dual reductive pairs". Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Representations of Real Reductive Lie Groups

Author : David A. Vogan
Publisher : Birkhauser
ISBN 13 :
Total Pages : 782 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Representations of Real Reductive Lie Groups by : David A. Vogan

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:

Real Reductive Groups I

Author : Nolan R. Wallach
Publisher : Academic Press
ISBN 13 : 0080874517
Total Pages : 439 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Real Reductive Groups I by : Nolan R. Wallach

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.

Lie Algebras and Lie Groups

Author : Jean-Pierre Serre
Publisher : Springer
ISBN 13 : 3540706348
Total Pages : 180 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Lie Algebras and Lie Groups by : Jean-Pierre Serre

Download or read book Lie Algebras and Lie Groups written by Jean-Pierre Serre and published by Springer. This book was released on 2009-02-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).

Representations of Compact Lie Groups

Author : T. Bröcker
Publisher : Springer Science & Business Media
ISBN 13 : 3662129183
Total Pages : 323 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Representations of Compact Lie Groups by : T. Bröcker

Download or read book Representations of Compact Lie Groups written by T. Bröcker and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

Representations of Finite Groups of Lie Type

Author : François Digne
Publisher : Cambridge University Press
ISBN 13 : 1108481485
Total Pages : 267 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Representations of Finite Groups of Lie Type by : François Digne

Download or read book Representations of Finite Groups of Lie Type written by François Digne and published by Cambridge University Press. This book was released on 2020-03-05 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups

Author : Armand Borel
Publisher : American Mathematical Soc.
ISBN 13 : 147041225X
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups by : Armand Borel

Download or read book Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.