Representation Theory Of Real Reductive Lie Groups
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Representation Theory Of Real Reductive Lie Groups
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Author : Wilfried Schmid, James Arthur, Peter E. Trapa
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-10-17
Representation Theory Of Real Reductive Lie Groups written by Wilfried Schmid, James Arthur, Peter E. Trapa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-17 with Representations of Lie groups categories.
The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference ``Representation Theory of Real Reductive Lie Groups'' held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature. This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields.
Representations Of Real Reductive Lie Groups
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Author : David A. Vogan
language : en
Publisher: Birkhauser
Release Date : 1981
Representations Of Real Reductive Lie Groups written by David A. Vogan and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Representation Theory Of Real Reductive Lie Groups
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Author : James Arthur
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Representation Theory Of Real Reductive Lie Groups written by James Arthur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMS-IMS-SIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."--BOOK JACKET.
Real Reductive Groups I
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Author : Nolan R. Wallach
language : en
Publisher: Academic Press
Release Date : 1988-03-01
Real Reductive Groups I written by Nolan R. Wallach and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-01 with Mathematics categories.
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.
Representation Theory And Harmonic Analysis On Semisimple Lie Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Representation Theory And Harmonic Analysis On Semisimple Lie Groups written by Paul J. Sally (Jr.) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This book brings together five papers that have been influential in the study of Lie groups. Though published more than 20 years ago, these papers made fundamental contributions that deserve much broader exposure. In addition, the subsequent literature that has subsumed these papers cannot replace the originality and vitality they contain. The editors have provided a brief introduction to each paper, as well as a synopsis of the major developments which have occurred in the area covered by each paper. Included here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's thesis is closely related to Trombi's paper insofar as both deal with harmonic analysis on real semisimple Lie groups, and, in particular, analysis on the Schwartz space of Harish-Chandra. Arthur's thesis is concerned with the image under the Fourier transform of the Schwartz space of a semisimple Lie group of real rank one, while Trombi's paper provides an expository account of the harmonic analysis associated to the decomposition of the Schwartz space under the regular representation. In his thesis, Osborne extends the Atiyah-Bott fixed point theorem for elliptic complexes to obtain a fixed point formula for complexes that are not elliptic. Schmid proves a generalization of the Borel-Weil theorem concerning an explicit and geometric realization of the irreducible representations of a compact, connected semisimple Lie group. Langlands's fundamental paper provides a classification of irreducible, admissible representations of real reductive Lie groups.
Unitary Representations Of Reductive Lie Groups
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Author : David A. Vogan
language : en
Publisher: Princeton University Press
Release Date : 1987-10-21
Unitary Representations Of Reductive Lie Groups written by David A. Vogan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-10-21 with Mathematics categories.
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.
Representations Of Real Reductive Lie Groups
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Author : David A. Vogan Jr
language : en
Publisher:
Release Date : 1981-01-01
Representations Of Real Reductive Lie Groups written by David A. Vogan Jr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
A large and powerful algebraic theory for the study of infinite dimensional representations of real reductive Lie groups has been developed. It already plays an important role even in purely analytic problems. This book describes the foundations of that theory, including some material not previously available in the literature. There are three major topics. The first is the Langlands construction and classification of the irreducible representations. This is done using a generalization of parabolic induction due to Zuckerman. The second topic is the analysis of reducibility in certain standard families of representations. Finally, conjectural character formulas for arbitrary irreducible representations are formulated. An interpretation of the formulas in term of Goresky-MacPherson cohomology, generalizing the Kazhdan-Lusztig conjecture for Verma modules is given.
Real Reductive Groups
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Author : Nolan R. Wallach
language : en
Publisher:
Release Date : 1988
Real Reductive Groups written by Nolan R. Wallach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Lie groups categories.
Lie Groups Lie Algebras And Representations
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Author : Brian Hall
language : en
Publisher: Springer
Release Date : 2015-05-11
Lie Groups Lie Algebras And Representations written by Brian Hall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-11 with Mathematics categories.
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Lie Groups Beyond An Introduction
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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Lie Groups Beyond An Introduction written by Anthony W. Knapp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.