Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula
Combinatorics
2022-02-08 v2 Algebraic Geometry
Abstract
We give a new proof that three families of polynomials coincide: the double Schubert polynomials of Lascoux and Sch\"utzenberger defined by divided difference operators, the pipe dream polynomials of Bergeron and Billey, and the equivariant cohomology classes of matrix Schubert varieties. All three families are shown to satisfy a "co-transition formula" which we explain to be some extent projectively dual to Lascoux' transition formula. We comment on the K-theoretic extensions.
Cite
@article{arxiv.1909.13777,
title = {Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula},
author = {Allen Knutson},
journal= {arXiv preprint arXiv:1909.13777},
year = {2022}
}
Comments
15 pp. For Bill Fulton's 80th birthday. v2 added section on partial pipe dreams