Endomorphism algebras of 2-row permutation modules in characteristic 3

Given r∈N, let λ be a partition of r with at most two parts. Let F be a field of characteristic 3. Write Mλ for the FSr-permutation module corresponding to the action of the symmetric group Sr on the cosets of the maximal Young subgroup Sλ. We construct a full set of central primitive idempotents in EndFSr(Mλ) in this case. We also determine the Young module corresponding to each primitive idempotent that we construct.