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.
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.
