Representations of Finite Groups of Lie Type

ISBN-13: 9781108722629 / Angielski / Miękka / 2020 / 264 str.

Francois Digne; Jean Michel

Opis

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.

Recenzje

'… clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical Gazette

Spis treści

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.