Young diagrams and intersection numbers for toric manifolds associated with Weyl chambers (Q2341050)

Let \(\Phi \) be a root system in the \(n-\)dimensional Euclidean space \(E\) with its inner product. Let \(\Delta (\Phi )\) be the fan determined by the collection of the Weyl chambers in \(E^*\), and \(X\) the toric manifold associated to \(\Delta (\Phi )\). The Weyl group naturally acts on \(X\). The aim of this paper is to study the intersection numbers of invariant divisors in \(X\). One of the main results is a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. It turns out that these numbers describe the ring structure of the cohomology of \(X\).