The intersection cohomology of Schubert varieties is a combinatorial invariant

Authors:
Francesco Brenti
Affiliations:
Dipartimento di Matematica, Universitá di Roma "Tor Vergata", Via della Ricerca Scientifica, 1, 00133 Roma, Italy
Venue:
European Journal of Combinatorics - Special issue: In honour of Alain Lascoux on the occasion of his 60th birthday
Year:
2004

Citing 3
Cited 3

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Abstract

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.