Equivariant symbol calculus for differential operators acting on forms

Details Equivariant symbol calculus for differential operators acting on forms Equivariant symbol calculus for differential operators acting on forms

2002-06-20

arxiv.org/abs/math/0206213v1

Lett. Math. Phys., 62, 219-232, 2002

Mathematics

Representation Theory

14 pages

Scientific paper

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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