Equivariant Symbol Calculus for Differential Operators Acting on Forms

Abstract

We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces $\mathcal{D}_p$ of differential operators transforming p-forms into functions, over $\mathbb{R}^n$. As an application, we classify the Vect(M)-equivariant maps from $\mathcal{D}_p$ to $\mathcal{D}_q$ 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.