Classification of smooth horizontal Schubert varieties
  We show that the smooth horizontal Schubert subvarieties of a rational homogeneous variety $G/P$ are homogeneously embedded cominuscule $G'/P'$, and are classified by subdiagrams of a Dynkin diagram. This generalizes the classification of smooth Schubert varieties in cominuscule $G/P$. 
Matt Kerr and Colleen Robles
math.AG math.RT