Gröbner bases for (partial) flag manifolds

On real flag manifolds with cup-length equal to its dimension

“…. By Borel's description from [2] (more precisely, its slight modification, see for example [7]), each class in H * (F ; Z 2 ) is a polynomial in Stiefel-Whitney of the vector bundles…”

“…In this section we give a necessary condition that a flag manifold with maximal cup-length needs to satisfy. This proof is based on a result from [7] (in fact, its mod 2 variant), where Gröbner bases for all flag manifolds were constructed.…”