Synopses & Reviews
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.
Review
"...clearly written, well-organized, and has proofs wherever possible. There are also many examples illustrating the theory." Bhama Srinivasan, Mathematical Reviews
Table of Contents
Background results; 1. Bruhat decomposition; 2. Reduced subgroups of maximal rank, centralisers and semisimple elements; 3. Rationality, Frobenius maps, Lang's theorem; 4. Generalized induction associated with a bimodule; 5. Mackey's theorem; 6. Harish-Chandra theory; Complements on RGL; 7. Duality of characters; 8. Steinberg characters; l-adic cohomology; 9. Deligne-Lusztig induction; 10. Character formulae and their complements in Deligne-Lusztig induction; 11. Geometric conjugation, Lusztig series.