The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at .
The skeleton of a reduced word and a correspondence of Edelman and Green.
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .
The weighted hook length formula. III: Shifted tableaux.
The Young diagrams of a pair of irreducible characters of with the same zero set on .
Truncations of random unitary matrices and Young tableaux.
Two-rowed -type Hecke algebra representations at roots of unity.