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Author: Marc Cabanes
Publisher: Springer Science & Business Media
ISBN: 1461241243
Category : Mathematics
Languages : en
Pages : 455
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Book Description
Finite reductive groups and their representations lie at the heart of group theory. This volume treats linear representations of finite reductive groups and their modular aspects together with Hecke algebras, complex reflection groups, quantum groups, arithmetic groups, Lie groups, symmetric groups and general finite groups.
Author: Marc Cabanes
Publisher: Springer Science & Business Media
ISBN: 1461241243
Category : Mathematics
Languages : en
Pages : 455
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Book Description
Finite reductive groups and their representations lie at the heart of group theory. This volume treats linear representations of finite reductive groups and their modular aspects together with Hecke algebras, complex reflection groups, quantum groups, arithmetic groups, Lie groups, symmetric groups and general finite groups.
Author: James E. Humphreys
Publisher: Cambridge University Press
ISBN: 9780521674546
Category : Mathematics
Languages : en
Pages : 260
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Book Description
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Author: Michael J. Collins
Publisher: Walter de Gruyter
ISBN: 3110889161
Category : Mathematics
Languages : en
Pages : 277
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Book Description
This book is an outgrowth of a Research Symposium on the Modular Representation Theory of Finite Groups, held at the University of Virginia in May 1998. The main themes of this symposium were representations of groups of Lie type in nondefining (or cross) characteristic, and recent developments in block theory. Series of lectures were given by M. Geck, A. Kleshchev and R. Rouquier, and their brief was to present material at the leading edge of research but accessible to graduate students working in the field. The first three articles are substantial expansions of their lectures, and each provides a complete account of a significant area of the subject together with an extensive bibliography. The remaining articles are based on some of the other lectures given at the symposium; some again are full surveys of the topic covered while others are short, but complete, research articles. The opportunity has been taken to produce a book of enduring value so that this is not a conference proceedings in the conventional sense. Material has been updated so that this book, through its own content and in its extensive bibliographies, will serve as an invaluable resource for all those working in the area, whether established researchers or graduate students who wish to gain a general knowledge of the subject starting from a single source.
Author: Meinolf Geck
Publisher: Cambridge University Press
ISBN: 1108808905
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.
Author: Michael John Collins
Publisher: Walter de Gruyter
ISBN: 9783110163674
Category : Mathematics
Languages : en
Pages : 284
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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: Meinolf Geck
Publisher: Cambridge University Press
ISBN: 1108489621
Category : Mathematics
Languages : en
Pages : 405
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Book Description
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.
Author: François Digne
Publisher: Cambridge University Press
ISBN: 1108481485
Category : Mathematics
Languages : en
Pages : 267
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Book Description
An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Author: George Lusztig
Publisher: American Mathematical Soc.
ISBN: 0821816896
Category : Mathematics
Languages : en
Pages : 58
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Book Description
Features notes that arose from a series of lectures given by the author at a CBMS Regional Conference held at Madison, Wisconsin, in August 1977. The purpose of the notes was to show how $1$-adic cohomology of algebraic varieties over fields of characteristic $p>1$ can be used to get information on the representations of finite Chevalley groups.
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
