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arXiv · 2602.14902

Galois automorphisms and blocks covering unipotent blocks

L. Ruhstorfer·A. A. Schaeffer Fry
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Abstract

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.

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L. Ruhstorfer, A. A. Schaeffer Fry. 2026-02-16. Galois automorphisms and blocks covering unipotent blocks. https://arxiv.org/abs/2602.14902

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