On the inductive blockwise Alperin weight condition for type $\mathsf{A}$

In this paper we prove the blockwise Alperin weight conjecture for finite special linear and unitary groups, for finite groups with abelian Sylow $3$-subgroups, and verify the inductive blockwise Alperin weight condition for certain cases of groups of type $\mathsf{A}$. We also give a classification for the 2-blocks of special linear and unitary groups.