A combinatorial proof that Schubert vs. Schur coefficients are nonnegative Institutional Repository Document uri icon

abstract

  • We give a combinatorial proof that the product of a Schubert polynomial by a Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses Assaf's theory of dual equivalence to show that a quasisymmetric function of Bergeron and Sottile is Schur-positive. By a geometric comparison theorem of Buch and Mihalcea, this implies the nonnegativity of Gromov-Witten invariants of the Grassmannian.

author list (cited authors)

  • Assaf, S., Bergeron, N., & Sottile, F.

complete list of authors

  • Assaf, Sami||Bergeron, Nantel||Sottile, Frank

Book Title

  • arXiv

publication date

  • May 2014