The intersection cohomology of Schubert varieties is a combinatorial invariant

We give an explicit and entirely poser-theoretic way to compute, for any permutation v, all the Kazhdan-Lusztig polynomials Px,y for x, y ≤ v, starting from the Bruhat interval [e, v] as an abstract poset. This proves, in particular, that the intersection cohomology of Schubert varieties depends only on the inclusion relations between the closures of its Schubert cells.

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