Skew Divided Difference Operators and Schubert Polynomials
Quantum Algebra
2008-04-24 v1 Classical Analysis and ODEs
Combinatorics
Abstract
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with positive integer coefficients.
Cite
@article{arxiv.0705.4546,
title = {Skew Divided Difference Operators and Schubert Polynomials},
author = {Anatol N. Kirillov},
journal= {arXiv preprint arXiv:0705.4546},
year = {2008}
}