  Cominuscule flag varieties generalize Grassmannians to other Lie types.
Schubert varieties in cominuscule flag varieties are indexed by posets of roots
labeled long/short. These labeled posets generalize Young diagrams. We prove
that Schubert varieties in potentially different cominuscule flag varieties are
isomorphic as varieties if and only if their corresponding labeled posets are
isomorphic, generalizing the classification of Grassmannian Schubert varieties
using Young diagrams by the last two authors. Our proof is type-independent.
