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.