  Let C(X) be the algebra generated by the curvature 2-forms of the standard
hermitian line bundles over the complex homogeneous manifold X=G/B. We
calculate the Hilbert polynomial of C(X) and give its presentation as a
quotient of a polynomial ring. In particular, we show the dimension of C(X) is
equal to the number of independent subsets of roots in the corresponding root
system. As a tool we study a more general algebra associated with a point on a
Grassmannian and calculate its Hilbert polynomial as well as its presentation
in terms of generators and relations.
