arXiv subjects

L. Ruhstorfer

Publications and source records attributed to L. Ruhstorfer.

4 recordsLinked to original sources

arXiv2026

Galois automorphisms and blocks covering unipotent blocks

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.

math.RT↗

arXiv2025

The Isaacs--Navarro Galois conjecture

We prove the original Galois refinement of the McKay conjecture, proposed by Isaacs--Navarro in 2002, providing an important subcase of the celebrated McKay--Navarro conjecture with several local-global consequences.

math.RT↗

arXiv2025

The McKay--Navarro conjecture for the prime 2

We complete the proof of the McKay--Navarro conjecture (also known as the Galois--McKay conjecture) for the prime 2, by completing the proof of the inductive McKay--Navarro conditions introduced by Navarro--Späth--Vallejo in this situation.

math.RT↗

arXiv2022

The inductive McKay-Navarro conditions for the prime 2 and some groups of Lie type

For a prime $\ell$, the McKay conjecture suggests a bijection between the set of irreducible characters of a finite group with $\ell'$-degree and the corresponding set for the normalizer of a Sylow $\ell$- subgroup. Navarro's refinement suggests that the values of the characters on either side of this bijection should also be related, proposing that the bijection commutes with certain Galois automorphisms. Recently, Navarro--Spaeth--Vallejo have reduced the McKay--Navarro conjecture to certain "inductive" conditions on finite simple groups. We prove that these inductive McKay--Navarro (also called the inductive Galois--McKay) conditions hold for the prime $\ell = 2$ for several groups of Lie type, including the untwisted groups without nontrivial graph automorphisms.

math.GR↗