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  • Print publication year: 2020
  • Online publication date: February 2020

4 - Unipotent Characters


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 give a 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.