Virtual Morita equivalences and Brauer character bijections

2024/01/24 by Xin Huang, Huang, Xin · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2401.13332

openalex publication_date 2024/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Brauer character bijections between blocks to virtual Morita equivalences. As a corollary, we obtain that Navarro's refinement of Alperin's weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and p-blocks of \rm SL₂(q) and \rm GL₂(q), where p|q.

Cited by

• Alperin's weight conjecture, Galois automorphisms, alternating sums, and functorial equivalences
• On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture

Related

• Descent of equivalences for blocks with Klein four defect groups
• Morita equivalence classes of blocks with extraspecial defect groups p₊¹⁺²
• Blocks with only one irreducible Brauer character orbit
• The blocks with four irreducible characters
• Morita equivalences and the inductive blockwise Alperin weight condition for type \mathsf A