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Equivariant symbol calculus for differential operators acting on forms

F. Boniver·S. Hansoul·P. Mathonet·N. Poncin
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Abstract

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. These results hold over a smooth manifold endowed with a flat projective structure. As an application, we classify the Vect(M)-equivariant maps from $D_p$ to $D_q$ over any manifold M, recovering and improving earlier results by N. Poncin. This provides the complete answer to a question raised by P. Lecomte about the extension of a certain intrinsic homotopy operator.

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BibTeXRIS

F. Boniver, S. Hansoul, P. Mathonet, N. Poncin. 2002-06-20. Equivariant symbol calculus for differential operators acting on forms. https://arxiv.org/abs/math/0206213

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