Schur flexibility of cominuscule Schubert varieties

Let $X = G / P$ be a cominuscule rational homogeneous variety. (Equivalently, $X$ admits the structure of a compact Hermitian symmetric space.) We say a Schubert class $\xi$ is Schur rigid if the only irreducible subvarieties $Y \subset X$ with homology class $[Y] \in \mathbb{Z}\xi$ are Schubert varieties. Robles and The identified a sufficient condition for $\xi$ to be Schur rigid. In this paper, we show that the condition is also necessary.

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Published 27 December 2013