Rigid Schubert classes in partial flag varieties

A Schubert class is called rigid if it can only be represented by Schubert varieties. The rigid Schubert classes have been classified in Grassmannians and orthogonal Grassmannians . In this paper, we study the rigidity problem in partial flag varieties (type A) and orthogonal partial flag varieties (type B and type D). In particular, we give numerical conditions that ensure a Schubert class is rigid.