  We use geometry to prove a number of new identities among the
Littlewood-Richardson coefficients for Schubert polynomials (Schubert classes
in a flag manifold). For many of these identities, there is a companion result
about the Bruhat order which should imply the identity, were it known how to
express these coefficients in terms of the Bruhat order. This analysis leads
the determination of many of these constants. We conclude with an outline of
geometric proofs for these identities.
