Reducedness of affine Grassmannian slices in type A
  We prove in type A a conjecture which describes the ideal of transversal slices to spherical Schubert varieties in the affine Grassmannian. As a corollary, we prove a modular description (due to Finkelberg-Mirkovi\'c) of the spherical Schubert varieties. 
Joel Kamnitzer, Dinakar Muthiah, Alex Weekes and Oded Yacobi
math.RT math.AG math.QA