Algebras of Curvature Forms on Homogeneous Manifolds

Alexander Postnikov (M.I.T., Cambridge, MA 02139, U.S.A.)
Boris Shapiro (University of Stockholm, Stockholm, S-10691, Sweden)
Mikhail Shapiro (Royal Institute of Technology, Stockholm, S-10044, Sweden)

March 4, 1998

Let~$\CC(X)$ be the algebra generated by the curvature two-forms of standard
holomorphic hermitian line bundles over the complex homogeneous manifold
$X=G/B$.
The cohomology ring of~$X$  is a quotient of~$\CC(X)$.  We calculate
the Hilbert polynomial of this algebra.  In particular, we show that the
dimension of~$\CC(X)$ is equal to the number of independent subsets of roots 
in the corresponding root system.