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Equivariance and extendibility in finite reductive groups with connected center

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Abstract

We show that several character correspondences for finite reductive groups \(G\) are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to \(G\) has connected center. The correspondences we consider are the so-called Jordan decomposition of characters introduced by Lusztig and the generalized Harish-Chandra theory of unipotent characters due to Broué–Malle–Michel. In addition we consider a correspondence giving character extensions, due to the second author, in order to verify the inductive McKay condition from Isaacs–Malle–Navarro for the non-abelian finite simple groups of Lie types \(^3\mathsf{D }_4,\mathsf{E }_8,\mathsf{F }_4,^2\mathsf{F }_4\), and \(\mathsf{G }_2\).

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Acknowledgments

We thank Michel Enguehard and Gunter Malle for useful remarks on the manuscript of this paper, and also Paul Fong for fruitful discussions.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Paris Diderot, Bâtiment Sophie Germain, 75205 , Paris Cedex 13, France

    Marc Cabanes

  2. Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 , Kaiserslautern, Germany

    Britta Späth

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  1. Marc Cabanes
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  2. Britta Späth
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Correspondence to Marc Cabanes.

Additional information

B. Späth has been supported by the Deutsche Forschungsgemeinschaft, SPP 1388.

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Cabanes, M., Späth, B. Equivariance and extendibility in finite reductive groups with connected center. Math. Z. 275, 689–713 (2013). https://doi.org/10.1007/s00209-013-1156-7

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