Orthogonal sets of Young symmetrizers

Young symmetrizers are primitive idempotents in the group algebra of the symmetric group Sn that are indexed in a natural way by Young tableaux. Although the Young symmetrizers corresponding to standard tableaux may be used to decompose the group algebra into a direct sum of minimal left ideals, they are not pairwise orthogonal in general. We pose the problem of finding maximum sets of pairwise orthogonal (but not necessarily standard) Young symmetrizers, and show in particular that it is possible to find (nonstandard) complete orthogonal sets for all partitions of n if and only if n⩽6.