Harish-Chandra Induction and Jordan Decomposition of Characters

2022/09/01 by Prashant Arote, Arote, Prashant, Manish Mishra +1
Chemistry · Mathematics · #20C33 #Advanced Algebra and Geometry #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2209.00574

openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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