  We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of
natural differential operators on a manifold equipped with a parabolic
geometry. This method permits us to define the additional structure of a
bilinear differential cup product on this sequence, satisfying a Leibniz rule
up to curvature terms. It is not associative, but is part of an A-infinity
algebra of multilinear differential operators, which we also obtain explicitly.
We illustrate the construction in the case of conformal differential geometry,
where the cup product provides a wide-reaching generalization of helicity
raising and lowering for conformally invariant field equations.
