The complexity of the Specht modules corresponding to hook partitions

Abstract

Let w be the p-weight of a hook partition μand E be an elementary abelian p-subgroup generated by w disjoint p-cycles. We compute the generic Jordan type of the Specht module corresponding to the partition μrestricted to E. In particular, we show that the complexity of the Specht module is precisely the p-weight of the partition μ.