Navarro's Brauer character Glauberman correspondence conjecture

Let \ell be a prime. Let AA act coprimely on a finite group GG by automorphisms, meaning that gcd(A,G)=1\gcd(|A|,|G|)=1. Write IBrA(G)\operatorname{IBr}_A(G) for the set of irreducible \ell-Brauer characters of GG fixed by AA, and let CG(A)\mathrm{C}_G(A) denote the subgroup of elements of GG centralized by AA.

Navarro's conjecture.

IBrA(G)=IBr(CG(A)).|\operatorname{IBr}_A(G)|=|\operatorname{IBr}(\mathrm{C}_G(A))|.

This is the proposed modular analogue of the Glauberman--Isaacs correspondence for ordinary irreducible characters. The supplied text does not state whether the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Zhicheng Feng and Britta Späth, “Unitriangular basic sets, Brauer characters and coprime actions”, arXiv:2111.13903 (2023).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.