Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer

2023/09/30 by A. A. Schaeffer Fry, Fry, A. A. Schaeffer, Jay Taylor +3
Chemistry · Mathematics · #20C33 #Advanced Algebra and Geometry #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2310.00237

openalex publication_date 2023/09/30 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28

Abstract

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this situation, we show that there is a unique Jordan decomposition satisfying conditions analogous to those of Digne--Michel's unique Jordan decomposition in the connected center case.

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