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Author : Jonathan Paul Brezin
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 43,6 Mb
Release : 1968
Category : Lie groups
ISBN : 9780821812792
Author : Ali Baklouti,Hidenori Fujiwara,Jean Ludwig
Publisher : Springer Nature
Page : 620 pages
File Size : 46,5 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 : Horst Leptin,Jean Ludwig
Publisher : Walter de Gruyter
Page : 213 pages
File Size : 48,9 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 : Louis Auslander,Calvin C. Moore
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 51,9 Mb
Release : 1966
Category : Group theory
ISBN : 9780821812624
Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 55,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author : David A. Vogan
Publisher : Princeton University Press
Page : 324 pages
File Size : 50,8 Mb
Release : 1987-10-21
Category : Mathematics
ISBN : 0691084823
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 : 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 : M. F. Atiyah
Publisher : Cambridge University Press
Page : 349 pages
File Size : 55,6 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 : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 468 pages
File Size : 48,7 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 : Elizabeth A. Tanner,R. Wilson
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401110785
During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.
Author : Hossein Abbaspour,Martin Moskowitz
Publisher : World Scientific Publishing Company
Page : 444 pages
File Size : 40,8 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 : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 464 pages
File Size : 40,6 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 : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 41,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Author : Anatoliĭ Moiseevich Vershik,Dmitriĭ Petrovich Zhelobenko
Publisher : CRC Press
Page : 576 pages
File Size : 54,9 Mb
Release : 1990
Category : Mathematics
ISBN : 2881246788
Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Author : Jeffrey Adams, David Vogan
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 50,9 Mb
Release : 2015-06-02
Category : Electronic
ISBN : 9781470423148
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.