Weight conjectures for Parker--Semeraro fusion systems

We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of Aut(G_2(3)), the principal 5-blocks of HN, BM, Aut(HN), Ly, the principal 7-block of M, and the... Show more