The intersection cohomology of Schubert varieties is a combinatorial invariant

We give an explicit and entirely poset-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. © 2003 Elsevier Ltd. All rights reserved. Facesti come quei che va di notte, che porta il lume dietro e sé non giova, ma dopo sé fa le persone dotte Dante, Divina Commedia Purg. XXII 67–69