Description
Book SynopsisOn its original publication, this book provided 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 entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the CurtisAlvis duality map and Mackey''s theorem and the results that can be deduced from it, before moving on to a discussion of DeligneLusztig induction and Lusztig''s Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.
Trade Review'… a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings
'… clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical Gazette
Table of Contents1. 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.
