Representations of Finite Groups of Lie Type by Jean Michel (English) Hardcover

Description: Representations of Finite Groups of Lie Type by Jean Michel, François Digne The original edition of this book, written for beginning graduate students, was 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 chapters on Hecke algebras and Green functions. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 Mackeys theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztigs 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. Author Biography 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. Table of Contents 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. 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 Promotional An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris. Long Description 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 Mackeys theorem and the results that can be deduced from it, before moving on to a discussion of Deligne-Lusztig induction and Lusztigs 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. Review Quote ... a useful resource for beginning graduate students in algebra as well as seasoned researchers. Mathematical Reviews Clippings Promotional "Headline" An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris. Description for Bookstore The original edition of this book, written for beginning graduate students, was 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 chapters on Hecke algebras and Green functions. Description for Library The original edition of this book, written for beginning graduate students, was 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 chapters on Hecke algebras and Green functions. Details ISBN1108481485 Author François Digne Publisher Cambridge University Press Series London Mathematical Society Student Texts Year 2020 ISBN-10 1108481485 ISBN-13 9781108481489 Format Hardcover Edition 2nd Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Replaces 9780521401173 DEWEY 512.482 Pages 264 Publication Date 2020-03-05 Affiliation Centre National de la Recherche Scientifique (CNRS), Paris Language English Series Number 95 UK Release Date 2020-03-05 AU Release Date 2020-03-05 NZ Release Date 2020-03-05 Illustrations Worked examples or Exercises; 6 Tables, black and white Edition Description 2nd Revised edition Alternative 9781108673655 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:168651502;

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