03576nam a22004695i 4500 978-0-85729-157-8 DE-He213 20260521092037.0 cr nn 008mamaa 101013s2011 xxk| s |||| 0|eng d 9780857291578 99780857291578 10.1007/978-0-85729-157-8 doi 512 23 Bonnafé, Cédric. author. Representations of SL2(Fq) [electronic resource] / by Cédric Bonnafé. London : Springer London, 2011. XXII, 186 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Algebra and Applications ; 13 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. 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'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. MATHEMATICS. ALGEBRA. GEOMETRY, ALGEBRAIC. GROUP THEORY. MATHEMATICS. ALGEBRA. ALGEBRAIC GEOMETRY. GROUP THEORY AND GENERALIZATIONS. SpringerLink (Online service) Springer eBooks Printed edition: 9780857291561 Algebra and Applications ; 13 http://dx.doi.org/10.1007/978-0-85729-157-8 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35896 35896 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 512 2025-10-06 08:44:42 2025-10-06 ER