Representations Of Finite Groups Of Lie Type
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Representations of Finite Groups of Lie Type
Author: François Digne
language: en
Publisher: Cambridge University Press
Release Date: 1991-04-26
The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.
Modular Representations of Finite Groups of Lie Type
Author: James E. Humphreys
language: en
Publisher: Cambridge University Press
Release Date: 2006
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
The Character Theory of Finite Groups of Lie Type
Author: Meinolf Geck
language: en
Publisher: Cambridge University Press
Release Date: 2020-02-27
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.