Equivariant symbol calculus for differential operators acting on forms

We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces D_p of differential operators transforming p-forms into functions, over R^n. As an application, we classify the Vect(M)-equivariant maps from D_p to D_q over a smooth manifold M, recovering and improving earlier results of N. Poncin. This provides the complete answer to a question raised by P. Lecomte about the extension of a certain intrinsic homotopy operator.