Representations of Finite Groups of Lie Type

List 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.

About the author

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.Jean Michel is Emeritus Director of Research at the Centre National de la Recherche Scientifique (CNRS), Paris. His research interests include reductive algebraic groups, in particular Deligne–Lusztig varieties, and Spetses and other objects attached to complex reflection groups. He has also co-authored with François Digne the monograph Foundations of Garside Theory (2015) and several notable papers on Deligne–Lusztig varieties.

Summary

The original edition of this book, written for beginning graduate students, was 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 chapters on Hecke algebras and Green functions.

Product details

• Authors: Francois Digne, François Digne, Francois (Universite De Picardie Jules Vern Digne, Francois (Universite de Picardie Jules Verne Digne, Francois (Universite de Picardie Jules Verne Amiens) Digne, Jean Michel, Jean (Centre National de la Recherche Scientifique (CNRS) Michel, Jean (Ecole Normale Superieure Paris) Michel
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.04.2020
• EAN: 9781108481489
• ISBN: 978-1-108-48148-9
• No. of pages: 264
• Series: London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Algebra / General, Mathematics