Galois-equivariant McKay bijections for primes dividing $q-1$
Representation Theory
2020-07-31 v1 Group Theory
Abstract
We prove that for most groups of Lie type, the bijections used by Malle and Spaeth in the proof of Isaacs-Malle-Navarro's inductive McKay conditions for the prime 2 and odd primes dividing q - 1 are also equivariant with respect to certain Galois automorphisms. In particular, this shows that these bijections are candidates for proving Navarro-Spaeth-Vallejo's recently-posited inductive Galois-McKay conditions. On the way, we show that several simple groups of Lie type satisfy the McKay--Navarro conjecture for the prime 2.
Keywords
Cite
@article{arxiv.2007.15575,
title = {Galois-equivariant McKay bijections for primes dividing $q-1$},
author = {A. A. Schaeffer Fry},
journal= {arXiv preprint arXiv:2007.15575},
year = {2020}
}