Unitary Representation Theory Of Exponential Lie Groups

Author : Horst Leptin,Jean Ludwig
Publisher : Walter de Gruyter
Page : 213 pages
File Size : 45,7 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110874235

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Unitary Representation Theory of Exponential Lie Groups by Horst Leptin,Jean Ludwig Pdf

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 : David A. Vogan
Publisher : Princeton University Press
Page : 324 pages
File Size : 45,8 Mb
Release : 1987-10-21
Category : Mathematics
ISBN : 0691084823

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Unitary Representations of Reductive Lie Groups by David A. Vogan Pdf

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 : Jonathan Paul Brezin
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 51,6 Mb
Release : 1968
Category : Lie groups
ISBN : 9780821812792

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Unitary Representation Theory for Solvable Lie Groups by Jonathan Paul Brezin Pdf

Author : Ali Baklouti,Hidenori Fujiwara,Jean Ludwig
Publisher : Springer Nature
Page : 620 pages
File Size : 54,6 Mb
Release : 2021-10-08
Category : Mathematics
ISBN : 9783030820442

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Representation Theory of Solvable Lie Groups and Related Topics by Ali Baklouti,Hidenori Fujiwara,Jean Ludwig Pdf

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 : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 46,9 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 45,7 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0387401229

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Lie Groups, Lie Algebras, and Representations by Brian C. Hall Pdf

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.

Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 40,7 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178

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Theory of Group Representations and Applications by Asim Orhan Barut,Ryszard R?czka Pdf

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Author : Elizabeth A. Tanner,R. Wilson
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401110785

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Noncompact Lie Groups and Some of Their Applications by Elizabeth A. Tanner,R. Wilson Pdf

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 : Anatoliĭ Moiseevich Vershik,Dmitriĭ Petrovich Zhelobenko
Publisher : CRC Press
Page : 576 pages
File Size : 48,7 Mb
Release : 1990
Category : Mathematics
ISBN : 2881246788

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Representation of Lie Groups and Related Topics by Anatoliĭ Moiseevich Vershik,Dmitriĭ Petrovich Zhelobenko Pdf

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 : M. F. Atiyah
Publisher : Cambridge University Press
Page : 349 pages
File Size : 41,8 Mb
Release : 1979
Category : Mathematics
ISBN : 9780521226363

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Representation Theory of Lie Groups by M. F. Atiyah Pdf

In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.

Author : Paul Sally,David A. Vogan
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 55,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821815267

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Representation Theory and Harmonic Analysis on Semisimple Lie Groups by Paul Sally,David A. Vogan Pdf

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.

Author : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 465 pages
File Size : 41,9 Mb
Release : 2014-12-05
Category : Mathematics
ISBN : 9784431552888

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Harmonic Analysis on Exponential Solvable Lie Groups by Hidenori Fujiwara,Jean Ludwig Pdf

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 : Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Publisher : Springer
Page : 268 pages
File Size : 54,9 Mb
Release : 2014-11-12
Category : Mathematics
ISBN : 9783319099347

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Developments and Retrospectives in Lie Theory by Geoffrey Mason,Ivan Penkov,Joseph A. Wolf Pdf

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. At the beginning, the top universities in California and Utah hosted the meetings, which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. These Lie theory workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. The contributors have all participated in these Lie theory workshops and include in this volume expository articles which will cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Author : Jeffrey Adams, David Vogan
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 49,5 Mb
Release : 2000-01-25
Category : Mathematics
ISBN : 0821886908

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Representation Theory of Lie Groups by Jeffrey Adams, David Vogan Pdf

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.

Author : Louis Auslander,Calvin C. Moore
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 47,8 Mb
Release : 1966
Category : Group theory
ISBN : 9780821812624

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Unitary Representations of Solvable Lie Groups by Louis Auslander,Calvin C. Moore Pdf