Representation Theory of Finite Reductive Groups [Hardcover]

A research level synthesis and reference in a key branch of modern algebra, first published in 2004.At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesising the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Throughout the text is illustrated by many examples and background i s 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.At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesising the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Throughout the text is illustrated by many examples and background i s 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.At the crossroads of representation theory, algebraic geometry and finite group theory, this book brings together many of the main concerns of modern algebra, synthesizing the past twenty-five years of research, by including some of the most remarkable achievements in the field. The text is illustrated throughout by many examples, and background material is provided by several introductory chapters on basic results as well as appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and a reference for all algebraists.Introduction; Notations and conventions; Part I. Representing Finite BN-Pairs: 1. Cuspidality in finite groups; 2. Finite BN-pairs; 3. Modular Hecke algebras for finite BN-pairs; 4. Modullc^