Wonderful Symmetric Varieties and Schubert Polynomials

TL;DR

This paper extends previous work to derive formulas for equivariant cohomology classes of specific orbits in flag varieties, leading to polynomial identities that factor sums of Schubert polynomials into products of linear forms.

Contribution

It provides new formulas for equivariant cohomology classes of spherical subgroup orbits and establishes polynomial identities involving Schubert polynomials.

Findings

Formulas for equivariant cohomology classes of closed orbits

Polynomial identities showing Schubert polynomial sums factor into linear products

Extension of prior results to broader classes of spherical subgroups

Abstract

Extending results of Wyser, we determine formulas for the equivariant cohomology classes of closed orbits of certain families of spherical subgroups of $GL_n$ on the flag variety $GL_n/B$. Putting this together with a slight extension of the results of Can-Joyce-Wyser, we arrive at a family of polynomial identities which show that certain explicit sums of Schubert polynomials factor as products of linear forms.