Equivariance and extendibility in finite reductive groups with connected center

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• 作者：Marc Cabanes (1)
  Britta Spth (2)
  
• 关键词：Finite groups of Lie type ; Jordan decomposition of characters ; Generalized Harish ; Chandra theory ; McKay conjecture ; 20C33 ; 20C15 ; 20C20
• 刊名：Mathematische Zeitschrift
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：275
• 期：3-4
• 页码：689-713
• 全文大小：
• 作者单位：Marc Cabanes (1)
  Britta Spth (2)
  
  1. Institut de Mathatiques de Jussieu, UniversitParis Diderot, Batiment Sophie Germain, 75205, Paris Cedex 13, France
  2. Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany
  
• ISSN：1432-1823

文摘

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 BrouCMalleichel. In addition we consider a correspondence giving character extensions, due to the second author, in order to verify the inductive McKay condition from Isaacsalleavarro 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 $\mathsf{G }_2$ .