05600048

j

05600048 Caselli, Fabrizio Diagonal invariants and the refined multimahonian distribution. J. Algebr. Comb. 30, No. 2, 193-213 (2009). 2009 Springer, Norwell, MA EN diagonal invariants symmetric groups descent sets Hilbert series Kronecker coefficients Robinson-Schensted correspondence irreducible decompositions tensor products of irreducible representations

doi:10.1007/s10801-008-0159-7

Summary: Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence we deduce the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproducts are a purely combinatorial algorithm to describe the irreducible decomposition of the tensor product of two irreducible representations of the symmetric group, and new symmetry results on permutation enumeration with respect to descent sets.