Navarro's Brauer character Glauberman correspondence conjecture

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Let ℓ\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 IBr⁡A(G)\operatorname{IBr}_A(G) for the set of irreducible ℓ\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.

∣IBr⁡A(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.

References

Primary source

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

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