
Representations of Finite Groups of Lie Type
Cambridge University Press
2nd Edition
Published on 5. March 2020
Book
Hardback
264 pages
978-1-108-48148-9 (ISBN)
Description
On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne-Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.
Reviews / Votes
'... a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings '... clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical GazetteMore details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Edition type
Revised edition
Illustrations
Worked examples or Exercises; 6 Tables, black and white
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 20 mm
Weight
590 gr
ISBN-13
978-1-108-48148-9 (9781108481489)
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Schweitzer Classification
Other editions
Additional editions

Francois Digne | Jean Michel
Representations of Finite Groups of Lie Type
E-Book
03/2020
2nd Edition
Cambridge University Press
€84.49
Available for download

Francois Digne
Representations of Finite Groups of Lie Type
E-Book
03/2020
Cambridge University Press
€78.99
Available for download
Previous edition

Francois Digne | Jean Michel
Representations of Finite Groups of Lie Type
Book
04/1991
Cambridge University Press
€198.24
Article exhausted; check for reprint
Persons
François Digne is Emeritus Professor at the Université de Picardie Jules Verne, Amiens. He works on finite reductive groups, braid and Artin groups. He has also co-authored with Jean Michel the monograph Foundations of Garside Theory (2015) and several notable papers on Deligne-Lusztig varieties.
Author
Universite de Picardie Jules Verne, Amiens
Centre National de la Recherche Scientifique (CNRS), Paris
Content
1. Basic results on algebraic groups; 2. Structure theorems for reductive groups; 3. (B, N)-pairs; parabolic, Levi, and reductive subgroups; centralisers of semi-simple elements; 4. Rationality, the Frobenius endomorphism, the Lang-Steinberg theorem; 5. Harish-Chandra theory; 6. Iwahori-Hecke algebras; 7. The duality functor and the Steinberg character; 8. l-adic cohomology; 9. Deligne-Lusztig induction; the Mackey formula; 10. The character formula and other results on Deligne-Lusztig induction; 11. Geometric conjugacy and Lusztig series; 12. Regular elements; Gelfand-Graev representations; regular and semi-simple characters; 13. Green functions; 14. The decomposition of Deligne-Lusztig characters; References; Index.