Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements
Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements
We link Schubert varieties in the generalized flag manifolds with hyperplane arrangements. For an element of a Weyl group, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincaré polynomial of the corresponding Schubert variety if and only …