The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.
Author(s): François Digne, Jean Michel
Series: London Mathematical Society Student Texts
Publisher: Cambridge University Press
Year: 1991
Language: English
Pages: 163
Tags: Математика;Общая алгебра;Группы и алгебры Ли;Группы Ли;
Title Page......Page 1
Table of Contents......Page 2
Introduction......Page 3
0. Basic results on algebraic groups......Page 7
1. The Bruhat decomposition; parabolic subgroups......Page 21
2. Intersections of parabolic subgroups......Page 30
3. Rationality, Frobenius endomorphism......Page 35
4. Harish-Chandra induction and restriction......Page 47
5. The Mackey formula......Page 53
6. Harish-Chandra’s theory......Page 59
7. Further results on Harish-Chandra induction......Page 63
8. The duality functor......Page 65
9. The Steinberg character......Page 74
10. l-adic cohomology......Page 78
11. Deligne-Lusztig induction; the Mackey formula......Page 83
12. The character formula and other results......Page 92
13. Geometric conjugacy and Lusztig series......Page 102
14. Regular elements; Gelfand-Graev representations......Page 122
15. Examples......Page 146
Bibliography......Page 160
Index......Page 162
