  We study spherical Schubert varieties in the affine Grassmannian. These
Schubert varieties have a natural conjectural modular description due to
Finkelberg-Mirkovi\'c. This modular description is easily seen to be
set-theoretically correct, but it is not obviously scheme-theoretically
correct. We prove that this modular description is correct in many cases. We
also link this modular description to the reducedness conjecture from
Kamnitzer-Webster-Weekes-Yacobi for tranverse slices in the affine
Grassmannian.
