arXiv subjects

Qulei Fu

Publications and source records attributed to Qulei Fu.

3 recordsLinked to original sources

arXiv2025

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

The Galois Alperin weight (GAW) conjecture has been reduced to the inductive GAW condition for simple groups. We proceed in two steps to refine this reduction. First, we propose the blockwise Galois Alperin weight (BGAW) conjecture and define its associated inductive BGAW condition. Second, assuming the inductive GAW (respectively, BGAW) condition for simple groups, we establish a stronger version of the GAW (respectively, BGAW) conjecture in terms of central (respectively, block) isomorphism of H-triples.

math.GR↗

arXiv2023

A reduction theorem for the Navarro Alperin weight conjecture

The Alperin weight conjecture has been reduced to simple groups by Navarro and Tiep. In this paper, we investigate the Navarro Alperin weight conjecture, which includes Galois automorphisms and group automorphisms in comparison with the original version, and give a reduction to simple groups. As an application, we prove the conjecture for the finite groups with abelian Sylow 2-subgroups.

math.RT↗

arXiv2023

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

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.

math.GR↗