Sp6(2a) 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=Sp6(2a) is “good” for these reductions for the McKay conjecture, the Alperin weight conjecture, and their blockwise versions.