Equivariance and extendibility in finite reductive groups with connected center
Identifieur interne : 000028 ( Main/Exploration ); précédent : 000027; suivant : 000029Equivariance and extendibility in finite reductive groups with connected center
Auteurs : Marc Cabanes [France] ; Britta Sp Th [Allemagne]Source :
- Mathematische Zeitschrift [ 0025-5874 ] ; 2013-12-01.
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Abstract
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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DOI: 10.1007/s00209-013-1156-7
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Z.</title><idno type="ISSN">0025-5874</idno><idno type="eISSN">1432-1823</idno><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2013-12-01">2013-12-01</date><biblScope unit="volume">275</biblScope><biblScope unit="issue">3-4</biblScope><biblScope unit="page" from="689">689</biblScope><biblScope unit="page" to="713">713</biblScope></imprint><idno type="ISSN">0025-5874</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5874</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Finite groups of Lie type</term><term>Generalized Harish-Chandra theory</term><term>Jordan decomposition of characters</term><term>McKay conjecture</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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 $$\mathsf{G }_2$$ .</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Rhénanie-Palatinat</li><li>Île-de-France</li></region><settlement><li>Kaiserslautern</li><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Cabanes, Marc" sort="Cabanes, Marc" uniqKey="Cabanes M" first="Marc" last="Cabanes">Marc Cabanes</name></region><name sortKey="Cabanes, Marc" sort="Cabanes, Marc" uniqKey="Cabanes M" first="Marc" last="Cabanes">Marc Cabanes</name></country><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Sp Th, Britta" sort="Sp Th, Britta" uniqKey="Sp Th B" first="Britta" last="Sp Th">Britta Sp Th</name></region><name sortKey="Sp Th, Britta" sort="Sp Th, Britta" uniqKey="Sp Th B" first="Britta" last="Sp Th">Britta Sp Th</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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