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2 results

  • 11 - Geometric Conjugacy and the Lusztig Series

  • François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Representations of Finite Groups of Lie Type
    Published online:
    14 February 2020
    Print publication:
    05 March 2020, pp 161-195

  • Summary

    We show how geometric conjugacy can be viewed in terms of the dual group. We explain the centre of a semi-simple group in terms of the affine root system. We explain Lusztig’s Jordan decomposition of characters. We express the characters of the general linear and unitary groups in term of Deligne–Lusztig characters and give the character table of GL2.

  • 4 - Unipotent Characters

  • Meinolf Geck, Universität Stuttgart, Gunter Malle, Technische Universität Kaiserslautern, Germany
  • Book:
    The Character Theory of Finite Groups of Lie Type
    Published online:
    20 February 2020
    Print publication:
    27 February 2020, pp 271-362

  • Summary

    After collectiong some properties of irreducible representations of finite Coxeter groups we state and explain Lusztig‘s result on the decomposition of Deligne-Lusztig characters and then givea detailed exposition of the parametrisation and the properties of unipotent characters of finite reductive groups and related data like Fourier matrices and eigenvalues of Frobenius. We then describe the decomposition of Lusztig induction and collect the most recent results on its commutation with Jordan decomposition. We end the chapter with a survey of the character theory of finite disconnected reductive groups.