Sami Assaf: Multiplying Schubert polynomials and Schur functions


Abstract

One of the most fundamental problems in algebraic combinatorics is to find a positive combinatorial construction for the structure constants of Schubert polynomials. A special case of this is the Littlewood--Richardson rule for the structure constants of Schur functions, which appear as Grassmannian Schubert polynomials. In joint work with N. Bergeron and F. Sottile, we give a combinatorial construction for the Schubert expansion of a Schubert polynomials times a Schur function. In this talk, I'll review the combinatorics of the k-Bruhat interval that led Bergeron and Sottile to construct a new quasisymmetric function whose Schur expansion encodes these structure constants, and show how we used dual equivalence to get a combinatorial formula for the Schur coefficients.