  The article discusses an action of the center of G on the quantum cohomology
of G/P's constructed geometrically. It is shown how to recover Bertram's
Quantum Schubert Calculus from this action, and also a refinement of a formula
of Fulton and Woodward for the terms of the smallest order in the product of
two Schubert varieties in the Quantum cohomology of a Grassmannian. The results
date to July 2001, and are needed to pose a Quantum analogue of the Horn and
Saturation Conjectures.
