Wonderful Symmetric Varieties and Schubert Polynomials

Extending results of Wyser, we determine formulas for the equivariant cohomology classes of closed orbits of certain families of spherical subgroups of $G{L}_n$ on the flag variety $G{L}_n\mathrm{/}B$. 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.