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Representations of Finite Groups of Lie Type

2nd Edition


Part of London Mathematical Society Student Texts

  • Authors:
  • François Digne, Université de Picardie Jules Verne, Amiens
  • Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
  • Date Published: March 2020
  • availability: In stock
  • format: Paperback
  • isbn: 9781108722629

£ 37.99

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About the Authors
  • 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.

    • Adds to the successful first edition, giving a more complete explanation while remaining at the same level of exposition
    • Covers the basic theory of algebraic groups, Coxeter groups and root systems, Hecke algebras and Frobenius endomorphisms
    • Contains background information for beginning graduate students, based on a course taught at the University of Paris
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    Product details

    • Edition: 2nd Edition
    • Date Published: March 2020
    • format: Paperback
    • isbn: 9781108722629
    • length: 264 pages
    • dimensions: 227 x 153 x 15 mm
    • weight: 0.39kg
    • contains: 6 tables
    • availability: In stock
  • 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

  • Authors

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

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