The Character Theory of Finite Groups of Lie Type A Guided Tour Cambridge Studies in Advanced Mathematics Series

Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne?Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish?Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

1. Reductive groups and Steinberg maps; 2. Lusztig's classification of irreducible characters; 3. Harish–Chandra theories; 4. Unipotent characters; Appendix. Further reading and open questions; References; Index.

Meinolf Geck is Professor of Algebra at Universität Stuttgart. He works in the areas of algebraic groups and representation theory of finite groups and has (co-)authored books including An Introduction to Algebraic Geometry and Algebraic Groups (2003), Representations of Hecke Algebras at Roots of Unity (2011) and Representations of Reductive Groups (1998).
Gunter Malle is Professor of Mathematics at Technische Universität Kaiserslautern, Germany. He works in the area of representation theory of finite groups and he co-authored Linear Algebraic Groups and Finite Groups of Lie Type (2011) and Inverse Galois Theory (1999). Professor Malle received an ERC Advanced Grant on 'Counting conjectures' in 2012.