Infinite flags and Schubert polynomials

TL;DR

This paper explores Schubert polynomials through infinite-dimensional geometry, revealing positivity properties, expansions, and embeddings related to flag varieties and their cohomology.

Contribution

It introduces new geometric methods to analyze Schubert polynomials, including positivity results and embeddings of type C flag varieties.

Findings

Graham-positivity of coefficients in equivariant coproducts

Expansions of back-stable and enriched Schubert polynomials

Construction of a type C flag variety embedding

Abstract

We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety, and study the corresponding pullback map on (equivariant) cohomology rings.