On the Classification of Schubert Varieties in Partial Flag Varieties

Abstract: We generalize the classification of isomorphism classes of Schubert varieties from complete flag varieties G/B to a class of partial flag varieties G/P. In particular, we classify all Schubert varieties in G/P where P is a minimal parabolic subgroup, and all Schubert surfaces which are two-dimensional Schubert varieties. We also obtain several classes of isomorphisms of Schubert varieties in flag varieties G/P where P is a maximal parabolic subgroup. In particular, we find an upper bound of the number of isomorphism classes of Schubert threefolds which are three-dimensional Schubert varieties.