Unitary Representation Theory For Solvable Lie Groups
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Unitary Representation Theory For Solvable Lie Groups
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Author : Jonathan Paul Brezin
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Unitary Representation Theory For Solvable Lie Groups written by Jonathan Paul Brezin 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 1968 with Lie groups categories.
Unitary Representation Theory For Solvable Lie Groups
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Author : Jonathan Paul Brezin
language : en
Publisher:
Release Date : 1968
Unitary Representation Theory For Solvable Lie Groups written by Jonathan Paul Brezin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Representation Theory Of Solvable Lie Groups And Related Topics
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Author : Ali Baklouti
language : en
Publisher: Springer Nature
Release Date : 2021-10-08
Representation Theory Of Solvable Lie Groups And Related Topics written by Ali Baklouti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-08 with Mathematics categories.
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.
Representations Of Solvable Lie Groups
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Author : Didier Arnal
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-08
Representations Of Solvable Lie Groups written by Didier Arnal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-08 with Mathematics categories.
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.
Representation Theory Of Lie Groups
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Author : Jeffrey Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-02
Representation Theory Of Lie Groups written by Jeffrey Adams 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 2015-06-02 with Mathematics categories.
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.
Harmonic Analysis On Exponential Solvable Lie Groups
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Author : Hidenori Fujiwara
language : en
Publisher: Springer
Release Date : 2014-12-05
Harmonic Analysis On Exponential Solvable Lie Groups written by Hidenori Fujiwara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Mathematics categories.
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.
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference
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Author : Takeshi Kawazoe
language : en
Publisher: World Scientific
Release Date : 1992-08-07
Representation Theory Of Lie Groups And Lie Algebras Proceedings Of Fuji Kawaguchiko Conference written by Takeshi Kawazoe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-07 with categories.
The proceedings in this volume covers recent developments of representation theory of real Lie groups, Lie algebras, harmonic analysis on homogeneous spaces, their applications and related topics.
Unitary Representation Theory Of Exponential Lie Groups
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Author : Horst Leptin
language : en
Publisher: Walter de Gruyter
Release Date : 1994
Unitary Representation Theory Of Exponential Lie Groups written by Horst Leptin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, 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 interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Unitary Representations Of Solvable Lie Groups
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Author : Louis Auslander
language : en
Publisher:
Release Date : 1971
Unitary Representations Of Solvable Lie Groups written by Louis Auslander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Lie groups categories.
In this monograph, we are going to treat some aspects of the unitary representation theory of solvable Lie groups. One of the fundamental questions one can raise about any locally compact group or C* algebra is that of determining when it is type I and to try to determine the structure of the set of equivalence classes of its irreducible representations. It is this and closely related questions which will occupy us here. In the course of this investigation, we will have to make use of a rather elaborate theory of infinite dimensional unitary representations of groups and algebras, and have thus included a rather lengthly expository introduction.
An Introduction To Lie Groups And Lie Algebras
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Author : Alexander Kirillov, Jr
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-30
An Introduction To Lie Groups And Lie Algebras written by Alexander Kirillov, Jr and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with Mathematics categories.
This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.