Descent of equivalences for blocks with Klein four defect groups

2021/06/07 by Xin Huang, Huang, Xin · 2 citations
Computer Science · Mathematics · #20C20 #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2106.03809

openalex publication_date 2021/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the splendid Rickard complexes for blocks with Klein four defect groups constructed by Rickard and Linckelmann descend to non-split fields. As a corollary, Navarro's refinement of the Alperin-McKay conjecture holds for blocks with a Klein four defect group. We also prove that splendid Morita equivalences between blocks and their Brauer correspondents (if exist) descend to non-split situations.

Cited by

• On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture
• The strengthened Broué abelian defect group conjecture for \rm SL(2,pⁿ) and \rm GL(2,pⁿ)

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