Description: Representations of Finite Groups of Lie Type An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris. François Digne (Author), Jean Michel (Author) 9781108481489, Cambridge University Press Hardback, published 5 March 2020 264 pages 23.4 x 15.6 x 1.9 cm, 0.49 kg '… a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings 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. 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. Subject Areas: Algebra [PBF]
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BIC Subject Area 1: Algebra [PBF]
Item Height: 234 mm
Item Width: 156 mm
Series: London Mathematical Society Student Texts
Author: Jean Michel, Francois Digne
Publication Name: Representations of Finite Groups of Lie Type
Format: Hardcover
Language: English
Publisher: Cambridge University Press
Subject: Mathematics
Publication Year: 2020
Type: Textbook
Item Weight: 490 g
Number of Pages: 264 Pages
