Harish-Chandra Induction and Jordan Decomposition of Characters

Abstract

We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a cuspidal representation of a Levi subgroup is isomorphic to a unipotent counterpart. These results generalize the well known results for groups with connected center.

arXiv commentThe authors request withdrawal of this submission because arXiv:2605.03036 is a substantially revised and expanded version containing significant new results, major revisions, and restructuring. Maintaining both submissions may confuse readers; please refer to arXiv:2605.03036 for the most up-to-date version of this work.