Descent of splendid Rickard equivalences in alternating groups

2021/11/21 by Huang, Xin · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2111.10922

Abstract

We show that each block of an alternating group over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent. This provides new evidence for a refined version of Broué's abelian defect group conjecture proposed by Kessar and Linckelmann.

Cited by

• On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture

Related

• The strengthened Broué abelian defect group conjecture for \rm SL(2,pⁿ) and \rm GL(2,pⁿ)
• On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture
• Galois descent of splendid Rickard equivalences for blocks of p-nilpotent groups
• Brou 'e's abelian defect group conjecture holds for the double cover of\n the Higman-Sims sporadic simple group
• Blocks with only one irreducible Brauer character orbit