Pipe dreams for Schubert polynomials of the classical groups

TL;DR

This paper introduces a combinatorial framework using analogues of pipe dreams for Schubert polynomials of classical groups, enhancing understanding of their structure and providing new computational tools.

Contribution

It develops a novel combinatorial description of Schubert polynomials for classical groups using pipe dream analogues, extending previous models.

Findings

Provides combinatorial models for classical group Schubert polynomials

Extends pipe dream techniques to Weyl groups of classical types

Facilitates computation and analysis of these polynomials

Abstract

Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl groups of the classical types.