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Author : Louis Auslander,Calvin C. Moore
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 42,6 Mb
Release : 1966
Category : Group theory
ISBN : 9780821812624
Author : Jonathan Paul Brezin
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 52,7 Mb
Release : 1968
Category : Lie groups
ISBN : 9780821812792
Author : Ali Baklouti,Hidenori Fujiwara,Jean Ludwig
Publisher : Springer Nature
Page : 620 pages
File Size : 54,8 Mb
Release : 2021-10-08
Category : Mathematics
ISBN : 9783030820442
The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.
Author : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 463 pages
File Size : 45,9 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108428095
A complete and self-contained account of the basic theory of unitary group representations for graduate students and researchers.
Author : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 464 pages
File Size : 41,9 Mb
Release : 2020-04-08
Category : Mathematics
ISBN : 9781108651936
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.
Author : Horst Leptin,Jean Ludwig
Publisher : Walter de Gruyter
Page : 213 pages
File Size : 48,7 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110874235
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 54,5 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Author : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 468 pages
File Size : 53,5 Mb
Release : 2014-12-05
Category : Mathematics
ISBN : 9784431552888
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.
Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 43,6 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author : M. F. Atiyah
Publisher : Cambridge University Press
Page : 349 pages
File Size : 54,8 Mb
Release : 1979
Category : Mathematics
ISBN : 9780521226363
In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.
Author : Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 798 pages
File Size : 44,8 Mb
Release : 1982
Category : Mathematics
ISBN : 0821814419
Author : L. Pukanszky
Publisher : American Mathematical Soc.
Page : 149 pages
File Size : 48,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821810880
This book adds to the great body of research that extends back to A. Weil and E. P. Wigner on the unitary representations of locally compact groups and their characters, i.e. the interplay between classical group theory and modern analysis. The groups studied here are the connected Lie groups of general type (not necessarily nilpotent or semisimple). Final results reflect Kirillov's orbit method; in the case of groups that may be non-algebraic or non-type I, the method requires considerable sophistication. Methods used range from deep functional analysis (the theory of $C*$-algebras, factors from F. J. Murray and J. von Neumann, and measure theory) to differential geometry (Lie groups and Hamiltonian actions). This book presents for the first time a systematic and concise compilation of proofs previously dispersed throughout the literature. The result is an impressive example of the deepness of Pukanszky's work.
Author : Hossein Abbaspour,Martin Moskowitz
Publisher : World Scientific Publishing Company
Page : 444 pages
File Size : 41,6 Mb
Release : 2007-09-21
Category : Mathematics
ISBN : 9789813101562
This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or on lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped. The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.
Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642502750
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.
Author : A Barut,R Raczka
Publisher : World Scientific Publishing Company
Page : 740 pages
File Size : 55,8 Mb
Release : 1986-11-01
Category : Mathematics
ISBN : 9789813103870
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