Jordan decomposition commutes with Harish-Chandra induction for all finite connected reductive groups, via an auxiliary result on endomorphism algebras of induced cuspidals.
Sur les caract\`eres des groupes r\'eductifs finis \`a centre non connexe : applications aux groupes sp\'eciaux lin\'eaires et unitaires
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Harish-Chandra Induction and Jordan Decomposition of Characters
Jordan decomposition commutes with Harish-Chandra induction for all finite connected reductive groups, via an auxiliary result on endomorphism algebras of induced cuspidals.