RELATING SIMPLE MODULES IN WEIGHT 2 BLOCKS OF SYMMETRIC GROUPS

In this article, we study weight 2 blocks of symmetric groups for a fixed odd prime p, and the relationships between them. We first prove that all sources of simple modules from these blocks come either from S2p or Sp C2; since this latter group is easy to understand, this result gives another indication that the principal block of S2p is the ‘most complicated ’ block of weight 2. We then examine which simple modules for S2p share their source with a simple module from Sp C2. 1