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Harmonic Analysis And Representations Of Semisimple Lie Groups

Harmonic Analysis and Representations of Semisimple Lie Groups PDF

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Author: J.A. Wolf
Publisher: Springer Science & Business Media
ISBN: 940098961X
Size: 13.73 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 496
View: 2141

Book Description: This book presents the text of the lectures which were given at the NATO Advanced Study Institute on Representations of Lie groups and Harmonic Analysis which was held in Liege from September 5 to September 17, 1977. The general aim of this Summer School was to give a coordinated intro duction to the theory of representations of semisimple Lie groups and to non-commutative harmonic analysis on these groups, together with some glance at physical applications and at the related subject of random walks. As will appear to the reader, the order of the papers - which follows relatively closely the order of the lectures which were actually give- follows a logical pattern. The two first papers are introductory: the one by R. Blattner describes in a very progressive way a path going from standard Fourier analysis on IR" to non-commutative harmonic analysis on a locally compact group; the paper by J. Wolf describes the structure of semisimple Lie groups, the finite-dimensional representations of these groups and introduces basic facts about infinite-dimensional unitary representations. Two of the editors want to thank particularly these two lecturers who were very careful to pave the way for the later lectures. Both these chapters give also very useful guidelines to the relevant literature.


Representation Theory And Harmonic Analysis On Semisimple Lie Groups

Representation Theory and Harmonic Analysis on Semisimple Lie Groups PDF

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Author: Paul Sally
Publisher: American Mathematical Soc.
ISBN: 0821815261
Size: 65.35 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 350
View: 5162

Book Description: 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.


An Introduction To Harmonic Analysis On Semisimple Lie Groups

An Introduction to Harmonic Analysis on Semisimple Lie Groups PDF

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Author: V. S. Varadarajan
Publisher: Cambridge University Press
ISBN: 9780521663625
Size: 16.92 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 316
View: 7107

Book Description: Now in paperback, this graduate-level textbook is an excellent introduction to the representation theory of semi-simple Lie groups. Professor Varadarajan emphasizes the development of central themes in the context of special examples. He begins with an account of compact groups and discusses the Harish-Chandra modules of SL(2,R) and SL(2,C). Subsequent chapters introduce the Plancherel formula and Schwartz spaces, and show how these lead to the Harish-Chandra theory of Eisenstein integrals. The final sections consider the irreducible characters of semi-simple Lie groups, and include explicit calculations of SL(2,R). The book concludes with appendices sketching some basic topics and with a comprehensive guide to further reading. This superb volume is highly suitable for students in algebra and analysis, and for mathematicians requiring a readable account of the topic.


Physics Briefs

Physics Briefs PDF

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Author:
Publisher:
ISBN:
Size: 70.30 MB
Format: PDF, ePub, Mobi
Category : Physics
Languages : en
Pages :
View: 7002

Book Description:


Harmonic Analysis On Semi Simple Lie Groups I

Harmonic Analysis on Semi Simple Lie Groups I PDF

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Author: Garth Warner
Publisher: Springer Science & Business Media
ISBN: 364250275X
Size: 80.17 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 532
View: 5243

Book Description: The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.


Harmonic Analysis On Free Groups

Harmonic Analysis on Free Groups PDF

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Author: Figa-Talamanca
Publisher: CRC Press
ISBN: 9780824770426
Size: 31.10 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 168
View: 3637

Book Description: This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.


Unitary Representations And Harmonic Analysis

Unitary Representations and Harmonic Analysis PDF

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Author: M. Sugiura
Publisher: Elsevier
ISBN: 9780080887593
Size: 33.46 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 451
View: 4832

Book Description: The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.


Theory Of Group Representations And Applications

Theory of Group Representations and Applications PDF

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Author: A Barut
Publisher: World Scientific Publishing Company
ISBN: 9813103876
Size: 60.12 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 740
View: 5071

Book Description: The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy


Representations Of Solvable Lie Groups

Representations of Solvable Lie Groups PDF

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Author: Didier Arnal
Publisher: Cambridge University Press
ISBN: 1108651933
Size: 79.80 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages :
View: 7687

Book Description: The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.


Symmetries And Laplacians

Symmetries and Laplacians PDF

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Author: David Gurarie
Publisher: Courier Corporation
ISBN: 0486462889
Size: 35.84 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 453
View: 385

Book Description: Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.