Abstract
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 − λ1,the only possible non trivial composition factor of 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.
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