An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence

Qulei Fu

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arXiv · 2311.06471

An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence

Qulei Fu

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Abstract

The Glauberman correspondence and its generalisation, the Dade--Glauberman--Nagao (DGN) correspondence, play an important role in studying local-global counting conjectures and their reductions to (quasi-)simple groups. These reduction theorems require an additional set of compatibility conditions for the DGN correspondence. In this paper, we prove that there exists a bijection of irreducible Brauer characters above the DGN correspondence that is equivariant with Galois automorphisms and group automorphisms and preserves vertices. Our proof utilizes the framework of $\hH$-triples developed by Navarro--Sp\"ath--Vallejo. The results establish a reduction theorem for the Galois Alperin weight conjecture.

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Qulei Fu. 2023-11-11. An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence. https://arxiv.org/abs/2311.06471

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