2 9 Ju l 2 00 3 Elementary divisors of Gram matrices of certain

The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is induced by the morphism of Carter and Payne, as shown by means of Kleshchev's modular branching rule. This enables the Jantzen filtration to be calculated in this case as well. 3 At a large prime 22 AMS subject classification: 20C30.