The Character Theory of Finite Groups of Lie Type

A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.

The character theory of reductive groups over finite fields is a rich, complex and vast field, incorporating tools and methods from many mathematical areas. This book provides a contemporary treatment of the theory and is a useful reference for graduate students and researchers with a basic understanding of algebraic geometry.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.