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

2023/11/11 by Qulei Fu, Fu, Qulei · 1 citation
Mathematics · #Finite Group Theory Research #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2311.06471

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--Späth--Vallejo. The results establish a reduction theorem for the Galois Alperin weight conjecture.

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• A reduction theorem for the blockwise Navarro Alperin weight conjecture via H-triples

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