Representation Theory of Finite Reductive Groups
Author | : Marc Cabanes |
Publisher | : Cambridge University Press |
Total Pages | : 457 |
Release | : 2004-01-29 |
Genre | : Mathematics |
ISBN | : 0521825172 |
Publisher Description
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Author | : Marc Cabanes |
Publisher | : Cambridge University Press |
Total Pages | : 457 |
Release | : 2004-01-29 |
Genre | : Mathematics |
ISBN | : 0521825172 |
Publisher Description
Author | : Roger W. Carter |
Publisher | : Cambridge University Press |
Total Pages | : 203 |
Release | : 1998-09-03 |
Genre | : Mathematics |
ISBN | : 0521643252 |
This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Author | : Nolan R. Wallach |
Publisher | : Academic Press |
Total Pages | : 439 |
Release | : 1988-03-01 |
Genre | : Mathematics |
ISBN | : 0080874517 |
Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.
Author | : Wee Teck Gan |
Publisher | : World Scientific |
Total Pages | : 277 |
Release | : 2015-02-13 |
Genre | : Mathematics |
ISBN | : 9814651826 |
This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.
Author | : Jens Carsten Jantzen |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082184377X |
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.
Author | : Meinolf Geck |
Publisher | : EPFL Press |
Total Pages | : 472 |
Release | : 2007-05-07 |
Genre | : Mathematics |
ISBN | : 9780849392436 |
After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).
Author | : Martin Burrow |
Publisher | : Courier Corporation |
Total Pages | : 210 |
Release | : 2014-05-05 |
Genre | : Mathematics |
ISBN | : 0486145077 |
DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div
Author | : Trombi |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2013-03-13 |
Genre | : Science |
ISBN | : 1468467301 |
This volume is the result of a conference on Representation Theory of Reductive Groups held in Park City, Utah, April 16-20, 1982, under the auspices of the Department of Mathematics, University of Utah. Funding for the conference was provided by the National Science Foundation. The text includes a number of original papers together with expository articles on work already in print. It is hoped that the volume will be of use to both experts in the field and nonspecialists interested in obtaining some insight into the area. Principal organizers of the conference were Henryk Hecht, Dragan Mili~ie, and Peter Trombi. They would like to express their thanks to the National Science Foundation for their support, to the speakers for their diligence in submitting their manuscripts, and to Carla Curtis, Karen Edge, and Katherine Ruth, for typing the manuscripts which were contributed. v CONTENTS J. Arthur, Multipliers and a Paley-Wiener theorem for real reductive groups .......................................... .
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 | : Cédric Bonnafé |
Publisher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2010-10-08 |
Genre | : Mathematics |
ISBN | : 0857291572 |
Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects. The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.