Galois automorphisms and blocks covering unipotent blocks

Fuente: arXiv
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Main Authors: Ruhstorfer, L., Fry, A. A. Schaeffer
Format: Preprint
Published: 2026
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author Ruhstorfer, L.
Fry, A. A. Schaeffer
author_facet Ruhstorfer, L.
Fry, A. A. Schaeffer
contents In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple groups, which when combined with their results gives a new characterization of finite groups with a normal $\ell$-complement for a prime $\ell$. This leads us to study the distribution of characters in unipotent blocks of disconnected reductive groups and show that this is well-behaved under a generalization of $d$-Harish-Chandra theory. We go on to study the blockwise Galois--McKay (also known as the Alperin--McKay--Navarro) conjecture for the blocks of almost (quasi-)simple groups above unipotent blocks.
format Preprint
id arxiv_https___arxiv_org_abs_2602_14902
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Galois automorphisms and blocks covering unipotent blocks
Ruhstorfer, L.
Fry, A. A. Schaeffer
Representation Theory
Group Theory
20C15, 20C33, 20C20
In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple groups, which when combined with their results gives a new characterization of finite groups with a normal $\ell$-complement for a prime $\ell$. This leads us to study the distribution of characters in unipotent blocks of disconnected reductive groups and show that this is well-behaved under a generalization of $d$-Harish-Chandra theory. We go on to study the blockwise Galois--McKay (also known as the Alperin--McKay--Navarro) conjecture for the blocks of almost (quasi-)simple groups above unipotent blocks.
title Galois automorphisms and blocks covering unipotent blocks
topic Representation Theory
Group Theory
20C15, 20C33, 20C20
url https://arxiv.org/abs/2602.14902