Differential invariants and curved Bernstein-Gelfand-Gelfand sequences

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∞-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.