The complexity of the Specht modules corresponding to hook partitions

摘要

We show that the complexity of the Specht module corresponding to any hook partition is the p-weight of the partition. We calculate the variety and the complexity of the signed permutation modules. Let E_s be a representative of the conjugacy class containing an elementary abelian p-subgroup of a symmetric group generated by s disjoint p-cycles. We give formulae for the generic Jordan types of signed permutation modules restricted to E_s and of Specht modules corresponding to hook partitions μ restricted to E_s where s is the p-weight of μ.