Intersections of Schubert varieties (Q1355542)

The Schubert calculus on a Grassmannian is a very well known topic. In fact, intersection theory on a Grassmannian is done in an algebraic-combinatorial way via Schur polynomials. On a general flag manifold, a canonical cell decomposition and a duality result for the corresponding closures of the cells (i.e. the Schubert varieties) are known. However there is not much more knowledge about the intersection of arbitrary Schubert varieties. The goal of the paper under review is to study the intersection of Schubert varieties in the varieties of full flags. The main result of the paper, as the author says, may be thought as an analogue of the Pieri formula. Most of the paper is devoted to the algebraic-combinatorial methods developed to prove this key result, which is a first step in the full understanding of the whole intersection theory of flag varieties.