The complexity of the Specht modules corresponding to hook partitions

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 .