be the universal exact sequence of complex vector bundles, where $S\to \operatorname{Gr}(k,n)$ is the universal subbundle and $Q\to \operatorname{Gr}(k,n)$ is the universal quotient bundle. Fix a complete flag
with $\dim_{\mathbb C}F_i=i$. For each $j\in\{1,\dots,n-k\}$, define the special Schubert variety, equipped with its reduced complex subvariety structure, by