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

2025/12/17 by Feng, Zhicheng, Fu, Qulei, Zhou, Yuanyang
Mathematics · #Geometric and Algebraic Topology #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2512.15243

Abstract

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.

Citations

• Character triples and weights
• A reduction theorem for the Character Triple Conjecture
• A reduction theorem for the Galois Alperin weight conjecture
• An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence
• The Alperin Weight Conjecture and the Glauberman correspondence via character triples
• Brauer's Height Zero Conjecture
• The McKay Conjecture and central isomorphic character triples
• A reduction theorem for the Galois-McKay conjecture
• Clifford theory of characters in induced blocks

Cited by

• Towards the inductive McKay--Navarro Condition for groups of Lie type

Related

• A reduction theorem for the Galois Alperin weight conjecture
• Alperin's weight conjecture, Galois automorphisms, alternating sums, and functorial equivalences
• Inductive blockwise Alperin weight condition for type B and odd primes
• The Alperin Weight Conjecture and the Glauberman correspondence via character triples
• The inductive blockwise Alperin weight condition for G₂(q) and ³D₄(q)