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  3. The Character Theory of Finite Groups of Lie Type
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
February 2020
Print publication year:
2020
Online ISBN:
9781108779081
DOI:
https://doi.org/10.1017/9781108779081
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
Cambridge Studies in Advanced Mathematics (187)
Information

Book description

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.

Reviews

‘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 Source: Mathematical Reviews

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