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Local Representation Theory
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Book Synopsis Local Representation Theory by : J. L. Alperin
Download or read book Local Representation Theory written by J. L. Alperin and published by Cambridge University Press. This book was released on 1993-09-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Representation Theory of Compact and Locally Compact Groups by : Alain Robert
Download or read book Introduction to the Representation Theory of Compact and Locally Compact Groups written by Alain Robert and published by Cambridge University Press. This book was released on 1983-02-10 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Representation Theory of Finite Groups: a Guidebook by : David A. Craven
Download or read book Representation Theory of Finite Groups: a Guidebook written by David A. Craven and published by Springer Nature. This book was released on 2019-08-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Representation Theory of Finite Reductive Groups by : Marc Cabanes
Download or read book Representation Theory of Finite Reductive Groups written by Marc Cabanes and published by Cambridge University Press. This book was released on 2004-01-29 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Book Synopsis A Journey Through Representation Theory by : Caroline Gruson
Download or read book A Journey Through Representation Theory written by Caroline Gruson and published by Springer. This book was released on 2018-10-23 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Local Langlands Conjecture for GL(2) by : Colin J. Bushnell
Download or read book The Local Langlands Conjecture for GL(2) written by Colin J. Bushnell and published by Springer Science & Business Media. This book was released on 2006-08-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elements of the Representation Theory of the Jacobi Group by : Rolf Berndt
Download or read book Elements of the Representation Theory of the Jacobi Group written by Rolf Berndt and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump
Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Groups and Representations by : J.L. Alperin
Download or read book Groups and Representations written by J.L. Alperin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations by : Pavel I. Etingof
Download or read book Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 1998 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.
Book Synopsis Local Newforms for GSp(4) by : Brooks Roberts
Download or read book Local Newforms for GSp(4) written by Brooks Roberts and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. An appendix includes extensive tables about the results and the representations theory of GSp(4).
Book Synopsis Langlands Correspondence for Loop Groups by : Edward Frenkel
Download or read book Langlands Correspondence for Loop Groups written by Edward Frenkel and published by Cambridge University Press. This book was released on 2007-06-28 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Book Synopsis Siegel Modular Forms by : Ameya Pitale
Download or read book Siegel Modular Forms written by Ameya Pitale and published by Springer. This book was released on 2019-05-07 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Book Synopsis A Gentle Course in Local Class Field Theory by : Pierre Guillot
Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot and published by Cambridge University Press. This book was released on 2018-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained exposition of local class field theory for students in advanced algebra.
