Infinite flags and Schubert polynomials

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.

40 pages, 2 figures. v2: omit Section 10 from v1, about affine flag varieties and Grassmannians (this material is superseded by arXiv:2305.19895); improved positivity statements and examples in Section 8; other minor changes and typo corrections