Representations Of Finite And Compact Groups

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 45,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804537

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Representations of Finite and Compact Groups by Barry Simon Pdf

Barry Simon, I.B.M. Professor of Mathematics and Theoretical Physics at the California Institute of Technology, is the author of several books, including such classics as ""Methods of Mathematical Physics"" (with M. Reed) and ""Functional Integration and Quantum Physics"". This new book, based on courses given at Princeton, Caltech, ETH-Zurich, and other universities, is an introductory textbook on representation theory.According to the author, 'Two facets distinguish my approach. First, this book is relatively elementary, and second, while the bulk of the books on the subject is written from the point of view of an algebraist or a geometer, this book is written with an analytical flavor'. The exposition in the book centers around the study of representation of certain concrete classes of groups, including permutation groups and compact semi simple Lie groups. It culminates in the complete proof of the Weyl character formula for representations of compact Lie groups and the Frobenius formula for characters of permutation groups. Extremely well tailored both for a one-year course in representation theory and for independent study, this book is an excellent introduction to the subject which, according to the author, is unique in having 'so much innate beauty so close to the surface'.

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 42,6 Mb
Release : 2024-06-17
Category : Mathematics
ISBN : 082187196X

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Representations of Finite and Compact Groups by Barry Simon Pdf

This book is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups that would be of interest to research mathematicians and graduate students interested in group theory and generalizations, topological groups, and Lie groups. Representation theory is discussed on finite groups of rotations, permutation groups, and classical compact Lie groups. The Weyl character formula is proved.

Author : Alain Robert
Publisher : Cambridge University Press
Page : 217 pages
File Size : 40,7 Mb
Release : 1983-02-10
Category : Mathematics
ISBN : 9780521289757

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Introduction to the Representation Theory of Compact and Locally Compact Groups by Alain Robert Pdf

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 : Dmitriĭ Petrovich Zhelobenko
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 46,8 Mb
Release : 1973-01-01
Category : Mathematics
ISBN : 0821886649

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Compact Lie Groups and Their Representations by Dmitriĭ Petrovich Zhelobenko Pdf

Author : Charles Benedict Thomas
Publisher : Imperial College Press
Page : 158 pages
File Size : 54,5 Mb
Release : 2004
Category : Mathematics
ISBN : 1860944841

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Representations of Finite and Lie Groups by Charles Benedict Thomas Pdf

This book provides an introduction to representations of both finite and compact groups. The proofs of the basic results are given for the finite case, but are so phrased as to hold without change for compact topological groups with an invariant integral replacing the sum over the group elements as an averaging tool. Among the topics covered are the relation between representations and characters, the construction of irreducible representations, induced representations and Frobenius reciprocity. Special emphasis is given to exterior powers, with the symmetric group Sn as an illustrative example. The book concludes with a chapter comparing the representations of the finite group SL2(p) and the non-compact Lie group SL2(P).

Author : Jean Pierre Serre
Publisher : Unknown
Page : 170 pages
File Size : 43,8 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:806314847

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Linear Representations of Finite Groups by Jean Pierre Serre Pdf

Author : E.B. Vinberg
Publisher : Birkhäuser
Page : 151 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892742

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Linear Representations of Groups by E.B. Vinberg Pdf

This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.

Author : David A. Craven
Publisher : Springer Nature
Page : 294 pages
File Size : 46,8 Mb
Release : 2019-08-30
Category : Mathematics
ISBN : 9783030217921

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Representation Theory of Finite Groups: a Guidebook by David A. Craven Pdf

This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.

Author : A. V. Zelevinsky
Publisher : Springer
Page : 189 pages
File Size : 53,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387114

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Representations of Finite Classical Groups by A. V. Zelevinsky Pdf

Author : Emmanuel Kowalski
Publisher : American Mathematical Society
Page : 442 pages
File Size : 47,9 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409661

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An Introduction to the Representation Theory of Groups by Emmanuel Kowalski Pdf

Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.

Author : Peter Schneider
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 43,6 Mb
Release : 2012-11-27
Category : Mathematics
ISBN : 9781447148326

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Modular Representation Theory of Finite Groups by Peter Schneider Pdf

Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 49,9 Mb
Release : 2011-10-23
Category : Mathematics
ISBN : 9781461407768

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Representation Theory of Finite Groups by Benjamin Steinberg Pdf

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Author : David Arnold
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 43,5 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9781441987501

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Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold Pdf

The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

Author : T. Bröcker,T.tom Dieck
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 41,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662129180

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Representations of Compact Lie Groups by T. Bröcker,T.tom Dieck Pdf

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 : Jing-Song Huang
Publisher : World Scientific
Page : 206 pages
File Size : 46,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9810237251

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Lectures on Representation Theory by Jing-Song Huang Pdf

This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.