Overview
- Presents an introduction to ordinary and modular Deligne-Lusztig theory through the detailed study of an example: SL2(Fq)
- Will serve as a complimentary text to existing titles on Deligne-Lusztig theory
- Includes Rouquier's theorem on derived equivalences of geometric nature (with some unpublished improvements) but is simple enough to be read by graduate/Ph. D. students
- Includes supplementary material: sn.pub/extras
Part of the book series: Algebra and Applications (AA, volume 13)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
-
Front Matter
-
Preliminaries
-
Front Matter
-
-
Ordinary Characters
-
Front Matter
-
-
Complements
-
Front Matter
-
-
Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Representations of SL2(Fq)
Authors: Cédric Bonnafé
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-0-85729-157-8
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Limited 2011
Hardcover ISBN: 978-0-85729-156-1Published: 25 October 2010
Softcover ISBN: 978-1-4471-2599-0Published: 01 December 2012
eBook ISBN: 978-0-85729-157-8Published: 08 October 2010
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: XXII, 186
Topics: Algebra, Algebraic Geometry, Group Theory and Generalizations