The complexity of the Specht modules corresponding to hook partitions

摘要

Let w be the p-weight of a hook partition \mu and E be an elementary abelianp-subgroup generated by w disjoint p-cycles. We compute the generic Jordan typeof the Specht module corresponding to the partition \mu restricted to E. Inparticular, we show that the complexity of the Specht module is precisely thep-weight of the partition \mu.