LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512
Title	Representations of SL2(Fq) (EB) / by Cédric Bonnafé
Author	Bonnafé, Cédric
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2011.
Physical Details	XXII, 186 pages : online resource.
Series	Algebra and Applications ; 13
ISBN	9780857291578
Summary Note	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 provide 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:
Contents note	Part I Preliminaries -- Structure of SL2(Fq) -- The Geometry of the Drinfeld Curve -- Part II Ordinary Characters -- Harish-Chandra Induction -- Deligne-Lusztig Induction -- The Character Table -- Part III Modular Representations -- More about Characters of G and of its Sylow Subgroups -- Unequal Characteristic: Generalities -- Unequal Characteristic: Equivalences of Categories -- Unequal Characteristic: Simple Modules, Decomposition Matrices -- Equal Characteristic -- Part IV Complements -- Special Cases -- Deligne-Lusztig Theory: an Overview -- Part V Appendices -- A l-Adic Cohomology -- B Block Theory -- C Review of Reflection Groups.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-0-85729-157-8
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Geometry, Algebraic . Group theory . Group Theory and Generalizations . Authors: Bonnafé, Cédric . Corporate Authors: SpringerLink (Online service) . Series: Algebra and Applications . Classification: 512 .

Catalogue Display

Representations of SL2(Fq)

Reviews