Representations of Finite Groups of Lie Type
2nd Edition
Part of London Mathematical Society Student Texts
- Authors:
- François Digne, Université de Picardie Jules Verne, Amiens
- Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
- Date Published: April 2020
- availability: Available
- format: Paperback
- isbn: 9781108722629
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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.
Read more- Adds to the successful first edition, giving a more complete explanation while remaining at the same level of exposition
- Covers the basic theory of algebraic groups, Coxeter groups and root systems, Hecke algebras and Frobenius endomorphisms
- Contains background information for beginning graduate students, based on a course taught at the University of Paris
Reviews & endorsements
'… a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings
See more reviews'… clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical Gazette
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×Product details
- Edition: 2nd Edition
- Date Published: April 2020
- format: Paperback
- isbn: 9781108722629
- length: 264 pages
- dimensions: 227 x 153 x 15 mm
- weight: 0.39kg
- contains: 6 tables
- availability: Available
Table of Contents
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.
Related Books
related journals
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