Linear Representations Of Groups

Author : E.B. Vinberg
Publisher : Birkhäuser
Page : 151 pages
File Size : 49,8 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 : Jean Pierre Serre
Publisher : Unknown
Page : 170 pages
File Size : 51,9 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:806314847

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Linear Representations of Finite Groups by Jean Pierre Serre Pdf

Author : J.L. Alperin,Rowen B. Bell
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207993

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Groups and Representations by J.L. Alperin,Rowen B. Bell Pdf

A concise treatment of topics from group theory and representation theory for use in a one-term course. Focussing on the non-commutative side of the field, this advanced textbook emphasizes the general linear group as the most important group and example. Readers are expected to be familiar with groups, rings, and fields, and to have a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to introduce the reader to additional topics.

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 54,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

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Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 55,9 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 : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 55,6 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396

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A Course in Finite Group Representation Theory by Peter Webb Pdf

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Author : Alexander Kleshchev
Publisher : Cambridge University Press
Page : 293 pages
File Size : 48,9 Mb
Release : 2005-06-30
Category : Mathematics
ISBN : 9781139444064

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Linear and Projective Representations of Symmetric Groups by Alexander Kleshchev Pdf

The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own

Author : Ėrnest Borisovich Vinberg
Publisher : Birkhauser
Page : 146 pages
File Size : 54,6 Mb
Release : 1989
Category : Mathematics
ISBN : 0817622888

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Linear Representations of Groups by Ėrnest Borisovich Vinberg Pdf

Author : Richard S. Elman,Murray M. Schacher,V. S. Varadarajan
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 46,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851616

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Linear Algebraic Groups and Their Representations by Richard S. Elman,Murray M. Schacher,V. S. Varadarajan Pdf

This book contains the proceedings of the Conference on Linear Algebraic Groups and Their Representations, held at UCLA in March 1992. The central theme is the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics. Linear algebraic groups and their representations interface with a broad range of areas through diverse avenues--with algebraic geometry through moduli spaces, with classical invariant theory through group actions on polynomial rings, with enumerative and combinatorial geometry through flag manifolds, and with theoretical physics through Kac-Moody algebras and quantum groups. Collected here are both surveys and original contributions by eminent specialists, reflecting current developments in the subject. This book is one of the few available sources that brings together such a wide variety of themes under a single unifying perspective.

Author : M. A. Naimark
Publisher : Elsevier
Page : 464 pages
File Size : 42,9 Mb
Release : 2014-07-15
Category : Mathematics
ISBN : 9781483184982

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Linear Representations of the Lorentz Group by M. A. Naimark Pdf

Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.

Author : Gordon James,Martin Liebeck
Publisher : Cambridge University Press
Page : 436 pages
File Size : 40,6 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 9781139811057

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Representations and Characters of Groups by Gordon James,Martin Liebeck Pdf

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

Author : Rolf Berndt
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 47,6 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9783834894014

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Representations of Linear Groups by Rolf Berndt Pdf

This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view.

Author : Martin Burrow
Publisher : Academic Press
Page : 196 pages
File Size : 46,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483258218

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Representation Theory of Finite Groups by Martin Burrow Pdf

Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

Author : Peter Schneider
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 55,5 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 : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494587

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Linear Representations of Finite Groups by Jean-Pierre Serre Pdf

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.