Abstract
It is well known that many geometric properties of Schubert varieties of type A (and others) can be interpreted combinatorially. Given two permutations w,x∈Sn we give a combinatorial consequence of the property that the smooth locus of the Schubert variety Xw contains the Schubert cell Yx. This provides a necessary ingredient for the interpretation of recent representation-theoretic results of the author with Mínguez in terms of identities of Kazhdan–Lusztig polynomials.
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