Representations of Finite Groups of Lie Type

Representations of Finite Groups of Lie Type

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Description

This book is based on a graduate course taught at the University of Paris. 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 emphasise 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.show more

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Review quote

"...clearly written, well-organized, and has proofs wherever possible. There are also many examples illustrating the theory." Bhama Srinivasan, Mathematical Reviewsshow more

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.show more