We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[Z1 xn, y1,.. . , yn] in two sets of variables by the ideal generated by all Sn invariant polynomialsâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1993

We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assumingâ€¦ (More)

In an earlier paper [13], we showed that the Hilbert scheme of points in the plane Hn = Hilb(C) can be identified with the Hilbert scheme of regular orbits C//Sn. Using this result, together with aâ€¦ (More)

This work is gratefully dedicated to Dominique Foata for his inspiring and pioneering work in algebraic combinatorics. We hope that he will nd it to be in harmony with the Lotharingian spirit whichâ€¦ (More)

The Hilbert scheme of points in the plane Hn = Hilb(C2) is an algebraic variety which parametrizes finite subschemes S of length n in C. To each such subscheme S corresponds an n-element multiset, orâ€¦ (More)

The task of a theory of Schubert polynomials is to produce explicit representatives for Schubert classes in the cohomology ring of a flag variety, and to do so in a manner that is as natural asâ€¦ (More)

Let Rn be the ring of coinvariants for the diagonal action of the symmetric group Sn. It is known that the character of Rn as a doubly-graded Sn module can be expressed using the Frobeniusâ€¦ (More)

We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[x1, . . . , xn, y1, . . . , yn] in two sets of variables by the ideal generated by all Sn invariantâ€¦ (More)