Classification of smooth horizontal Schubert varieties

Abstract

We show that the smooth horizontal Schubert subvarieties of a rational homogeneous variety $G/P$ are homogeneously embedded cominuscule $G^{\prime }/P^{\prime }$, and are classified by subdiagrams of a Dynkin diagram. This generalizes the classification of smooth Schubert varieties in cominuscule $G/P$.

replaces sections 3 and 4 of arXiv:1407.4507v1, which were eliminated in its revision; comments welcome