Representation Theory of Finite Reductive Groups (Relié)

At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesizing the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes : first, applications of étale cohomology, leading, via notions of twisted induction, unipotent characters and Lusztig's approach to the Jordan decomposition of characters, to the proof of the recent Bonnafé-Rouquier theorems.
The second is a straightforward and simplified account of the Dipper-James theorems relating irreducible characters and modular representations, while introducing modular Hecke and Schur algebras. The final theme is local representation theory. One of the main results here is the authors' version of Fong-Srinivasan theorems showing the relations between twisted induction and blocks of modular representations.
Throughout, the text is illustrated by many examples ; background is provided by several introductory chapters on basic results, and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.