Representations of Finite Groups of Lie Type

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François Digne (Université de Picardie Jules Verne, Amiens) Jean Michel (Centre National de la Recherche Scientifique (CNRS), Paris)

Representations of Finite Groups of Lie Type

François Digne (Université de Picardie Jules Verne, Amiens), Jean Michel (Centre National de la Recherche Scientifique (CNRS), Paris)

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English

Cambridge University Press
05 March 2020

Algebra

Series: London Mathematical Society Student Texts

On 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 Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig 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.

By: François Digne (Université de Picardie Jules Verne Amiens), Jean Michel (Centre National de la Recherche Scientifique (CNRS), Paris)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 234mm, Width: 156mm, Spine: 19mm
Weight: 490g
ISBN: 9781108481489
ISBN 10: 1108481485
Series: London Mathematical Society Student Texts
Pages: 264
Publication Date: 05 March 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

François Digne is Emeritus Professor at the Université de Picardie Jules Verne, Amiens. He works on finite reductive groups, braid and Artin groups. He has also co-authored with Jean Michel the monograph Foundations of Garside Theory (2015) and several notable papers on Deligne–Lusztig varieties. Jean Michel is Emeritus Director of Research at the Centre National de la Recherche Scientifique (CNRS), Paris. His research interests include reductive algebraic groups, in particular Deligne–Lusztig varieties, and Spetses and other objects attached to complex reflection groups. He has also co-authored with François Digne the monograph Foundations of Garside Theory (2015) and several notable papers on Deligne–Lusztig varieties.

Reviews for Representations of Finite Groups of Lie Type

'… 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