Representation Theory Of Lie Groups And Lie Algebras - Proceedings Of Fuji-kawaguchiko Conference PDF Download
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Author: Takeshi Kawazoe
Publisher: World Scientific
ISBN: 981455443X
Category :
Languages : en
Pages : 256
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Book Description
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.
Author: Takeshi Kawazoe
Publisher: World Scientific
ISBN: 981455443X
Category :
Languages : en
Pages : 256
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Book Description
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.
Author:
Publisher:
ISBN:
Category : Representations of Lie algebras
Languages : en
Pages : 245
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Book Description
Author: Takeshi Kawazoe
Publisher:
ISBN: 9789814537162
Category : MATHEMATICS
Languages : en
Pages : 256
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Book Description
Author: Ali Baklouti
Publisher: Springer Nature
ISBN: 3030820440
Category : Mathematics
Languages : en
Pages : 620
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Book Description
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: V.S. Varadarajan
Publisher: Springer Science & Business Media
ISBN: 1461211263
Category : Mathematics
Languages : en
Pages : 444
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Book Description
This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.
Author: Hidenori Fujiwara
Publisher: Springer
ISBN: 443155288X
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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: Brian C. Hall
Publisher: Springer Science & Business Media
ISBN: 9780387401225
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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: K. Trimeche
Publisher: Nova Publishers
ISBN: 9781600210143
Category : Mathematics
Languages : en
Pages : 178
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Book Description
These proceedings consist of ten carefully refereed and selected papers which were presented at the 12th symposium of Tunisian Mathematical Society held on March 18-23, 2004 in Mahdia (Tunisia). This symposium was one of the largest international meeting on Mathematics in Tunisia. A total of 200 participants from several countries attended to the meeting. In addition to the plenary, invited and contributed talks, there was a panel discussion on future research directions and problems in various areas of mathematics.
Author: B.P. Komrakov
Publisher: Springer Science & Business Media
ISBN: 9401152586
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.
Author: Ali Baklouti
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110765306
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.
