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$Sp_6(2^a)$ is "Good" for the McKay, Alperin Weight, and Related Local-Global Conjectures

The so-called "local-global" conjectures in the representation theory of finite groups relate the representation theory of $G$ to that of certain proper subgroups, such as the normalizers of particular $p$-groups. Recent results by several authors reduce some of these conjectures to showing that a certain collection of stronger conditions holds for all finite simple groups. Here, we show that $G=Sp_6(2^a)$ is "good" for these reductions for the McKay conjecture, the Alperin weight conjecture, and their blockwise versions.