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  3. Representations of Finite Groups of Lie Type
    2nd edition
    • François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
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  • Publisher:
    Cambridge University Press
    Publication date:
    14 February 2020
    05 March 2020
    ISBN:
    9781108673655
    DOI:
    https://doi.org/10.1017/9781108673655
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    • Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Student Texts (95)
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    • Selected: Paperback
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Student Texts (95)
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    Book 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 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.

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    Contents

    Contents
    • 3 - (B,N)-Pairs; Parabolic, Levi, and Reductive Subgroups; Centralisers of Semi-simple Elements
      pp 39-58
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