Equivariance and extendibility in finite reductive groups with connected center

We show that several character correspondences for finite reductive groups are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to has connected center. The correspondences we consider are the so-called Jordan decomposition of...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 275; no. 3-4; pp. 689 - 713
Main Authors Cabanes, Marc, Späth, Britta
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013
Subjects
Mathematics
Mathematics and Statistics
Jordan decomposition of characters
Finite groups of Lie type
20C33
20C20
Generalized Harish-Chandra theory
20C15
McKay conjecture
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Summary:We show that several character correspondences for finite reductive groups are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to 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 , and .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-013-1156-7