Descent of splendid Rickard equivalences in ${\mathrm{GL}}_n(q)$

Abstract

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Broué's abelian defect group conjecture holds for unipotent $\ell$-blocks of ${\mathrm{GL}}_n(q)$, where $\ell \nmid q$. We also give a sufficient condition on general $\ell$-blocks of ${\mathrm{GL}}_n(q)$ to satisfy the refined abelian defect group conjecture. We explain by an example that this sufficient condition does not hold in general.

the final version

Cited by in corpus (1)

• On endosplit $p$-permutation resolutions and Broué's conjecture for $p$-solvable groups