Local Representation Theory

Local Representation Theory PDF

Author: J. L. Alperin

Publisher: Cambridge University Press

Published: 1993-09-24

Total Pages: 198

ISBN-13: 9780521449267

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The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.

Introduction to the Representation Theory of Compact and Locally Compact Groups

Introduction to the Representation Theory of Compact and Locally Compact Groups PDF

Author: Alain Robert

Publisher: Cambridge University Press

Published: 1983-02-10

Total Pages: 217

ISBN-13: 0521289750

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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.

A Course in Finite Group Representation Theory

A Course in Finite Group Representation Theory PDF

Author: Peter Webb

Publisher: Cambridge University Press

Published: 2016-08-19

Total Pages: 339

ISBN-13: 1107162394

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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.

Representation Theory of Finite Groups: a Guidebook

Representation Theory of Finite Groups: a Guidebook PDF

Author: David A. Craven

Publisher: Springer Nature

Published: 2019-08-30

Total Pages: 294

ISBN-13: 3030217922

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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.

A Journey Through Representation Theory

A Journey Through Representation Theory PDF

Author: Caroline Gruson

Publisher: Springer

Published: 2018-10-23

Total Pages: 223

ISBN-13: 3319982710

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This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

Local Representation Theory and Simple Groups

Local Representation Theory and Simple Groups PDF

Author: Radha Kessar

Publisher:

Published: 2018

Total Pages: 0

ISBN-13: 9783037191859

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"The book contains extended versions of seven short lecture courses given during a semester programme on "Local Representation Theory and Simple Groups" held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These focused on modular representation theory of finite groups, modern Clifford theoretic methods, the representation theory of finite reductive groups, as well as on various applications of character theory and representation theory, for example to base sizes and to random walks. These lectures are intended to form a good starting point for graduate students and researchers who wish to familiarize themselves with the foundations of the topics covered here. Furthermore they give an introduction to current research directions, including the state of some open problems in the field"--Page 4 of cover.

The Local Langlands Conjecture for GL(2)

The Local Langlands Conjecture for GL(2) PDF

Author: Colin J. Bushnell

Publisher: Springer Science & Business Media

Published: 2006-08-29

Total Pages: 352

ISBN-13: 354031511X

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The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

Elements of the Representation Theory of the Jacobi Group

Elements of the Representation Theory of the Jacobi Group PDF

Author: Rolf Berndt

Publisher: Springer Science & Business Media

Published: 2012-01-05

Total Pages: 225

ISBN-13: 303480282X

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Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.

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