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Combinatorial aspects of multivariate diagonal invariants of the symmetricgroup are studied. As a consequence it is proved the existence of amultivariate extension of the classical Robinson-Schensted correspondence.Further byproduct are a pure combinatorial algorithm to describe theirreducible decomposition of the tensor product of two irreduciblerepresentations of the symmetric group, and new symmetry results on permutationenumeration with respect to descent sets.

Diagonal invariants and the refined multimahonian distribution