Jordan decomposition for weights and the blockwise Alperin weight conjecture

Abstract

The Alperin weight conjecture was reduced to simple groups by the work of Navarro–Tiep and Späth. To prove Alperin weight conjecture, it suffices to show that all finite non-abelian simple groups are BAW-good. We reduce the verification of the inductive conditions for groups of Lie type in non-defining characteristic to quasi-isolated blocks.