Bumpless pipe dream RSK, growth diagrams, and Schubert structure constants

TL;DR

This paper develops a combinatorial framework using bumpless pipe dreams and growth diagrams to compute Schubert structure constants in flag varieties, providing new tools for Schubert calculus.

Contribution

It introduces analogs of RSK insertion for Schubert calculus, connecting bumpless pipe dreams with growth diagrams to compute structure constants.

Findings

Provides a combinatorial rule for Schubert structure constants in the separated descent case.

Establishes a new insertion algorithm using bumpless pipe dreams for Schubert calculus.

Links growth diagrams with Schubert structure constants, enhancing computational methods.

Abstract

We introduce analogs of left and right RSK insertion for Schubert calculus of complete flag varieties. The objects being inserted are certain biwords, the insertion objects are bumpless pipe dreams, and the recording objects are decorated chains in Bruhat order. As an application, we adopt Lenart's growth diagrams of permutations to give a combinatorial rule for Schubert structure constants in the separated descent case.