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| Author | : James E. Humphreys |
| Publisher | : Cambridge University Press |
| Total Pages | : 260 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9780521674546 |
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
| Author | : James E. Humphreys |
| Publisher | : |
| Total Pages | : 233 |
| Release | : 2006 |
| Genre | : Electronic books |
| ISBN | : 9781107367715 |
Comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
| Author | : François Digne |
| Publisher | : Cambridge University Press |
| Total Pages | : 267 |
| Release | : 2020-03-05 |
| Genre | : Mathematics |
| ISBN | : 1108481485 |
An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
| Author | : Roger William Carter |
| Publisher | : |
| Total Pages | : 156 |
| Release | : 1973 |
| Genre | : Lie groups |
| ISBN | : |
| Author | : Meinolf Geck |
| Publisher | : Cambridge University Press |
| Total Pages | : 406 |
| Release | : 2020-02-27 |
| Genre | : Mathematics |
| ISBN | : 1108808905 |
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 | : Peter Webb |
| Publisher | : Cambridge University Press |
| Total Pages | : 339 |
| Release | : 2016-08-19 |
| Genre | : Mathematics |
| ISBN | : 1107162394 |
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 | : Michael J. Collins |
| Publisher | : Walter de Gruyter |
| Total Pages | : 277 |
| Release | : 2011-07-11 |
| Genre | : Mathematics |
| ISBN | : 3110889161 |
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 | : Gunter Malle |
| Publisher | : Cambridge University Press |
| Total Pages | : 324 |
| Release | : 2011-09-08 |
| Genre | : Mathematics |
| ISBN | : 113949953X |
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
| Author | : Meinolf Geck |
| Publisher | : |
| Total Pages | : 47 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : David A. Craven |
| Publisher | : Springer Nature |
| Total Pages | : 294 |
| Release | : 2019-08-30 |
| Genre | : Mathematics |
| ISBN | : 3030217922 |
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.
