The Character Theory of Finite Groups of Lie Type
A Guided Tour

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

Meinolf Geck (Author), Gunter Malle (Author)

9781108489621, Cambridge University Press

Hardback, published 27 February 2020

404 pages, 35 tables
23.4 x 15.6 x 2.6 cm, 0.68 kg

'The book is very well written … the entire text is meticulously referenced and succeeds in giving a fascinating guided tour through this vast territory.' Donald L. White, Mathematical Reviews

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.

Subject Areas: Algebra [PBF]