An effective decomposition theorem for Schubert varieties

Given a Schubert variety S contained in Grassmannian Gk(Cl), we show how to obtain further information on the direct summands of derived pushforward Rπ⁎QS˜ given by application decomposition theorem suitable resolution singularities π:S˜→S. As by-product, Poincaré polynomial expressions are obtained along with an algorithm which computes unknown terms such and shows that actual number happens be less than supports decomposition.