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:<math>\dim({X_\lambda(\mathcal{V})}) = |\lambda|. </math>
An equivalent, but simpler characterization of the Schubert cell <math>X_\lambda(\mathcal{V})</math> may be given in terms of the [[flag manifold | dual complete flag]]
:<math> \tilde{\mathcal{V}}= (\tilde{V}_1 \subset \tilde{V}_2 \cdots \subset \tilde{V}_n = V),</math>
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