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| Author | : Eberhard Kaniuth |
| Publisher | : Cambridge University Press |
| Total Pages | : 359 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 052176226X |
A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.
| Author | : Alain Robert |
| Publisher | : Cambridge University Press |
| Total Pages | : 217 |
| Release | : 1983-02-10 |
| Genre | : Mathematics |
| ISBN | : 0521289750 |
Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.
| Author | : J. M.G. Fell |
| Publisher | : Academic Press |
| Total Pages | : 755 |
| Release | : 1988-05-01 |
| Genre | : Mathematics |
| ISBN | : 0080874452 |
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
| Author | : George Whitelaw Mackey |
| Publisher | : |
| Total Pages | : 184 |
| Release | : 1968 |
| Genre | : Science |
| ISBN | : |
| Author | : T. Bröcker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 323 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662129183 |
This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.
| Author | : Anthony W. Knapp |
| Publisher | : Princeton University Press |
| Total Pages | : 968 |
| Release | : 2016-06-02 |
| Genre | : Mathematics |
| ISBN | : 1400883938 |
This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.
| Author | : Gerald B. Folland |
| Publisher | : CRC Press |
| Total Pages | : 317 |
| Release | : 2016-02-03 |
| Genre | : Mathematics |
| ISBN | : 1498727158 |
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
| Author | : Eberhard Kaniuth |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 321 |
| Release | : 2018-07-05 |
| Genre | : Mathematics |
| ISBN | : 0821853651 |
The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
| Author | : Colin John Bushnell |
| Publisher | : Princeton University Press |
| Total Pages | : 330 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 9780691021140 |
This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N, F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.
| Author | : Didier Arnal |
| Publisher | : Cambridge University Press |
| Total Pages | : 464 |
| Release | : 2020-04-08 |
| Genre | : Mathematics |
| ISBN | : 1108651933 |
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.
