Equivariant Operators between some Modules of the Lie Algebra of Vector Fields

The space D p of differential operators of order ≤ k, from the differential forms of degree p of a smooth manifold M into the functions of M, is a module over the Lie algebra of vector fields of M, when it’s equipped with the natural Lie derivative. In this paper, we compute all equivariant i.e. intertwining operators T : D p → D l q and conclude that the preceding modules of differential operators are never isomorphic. We also answer a question of P. Lecomte, who observed that the restriction of some homotopy operator—introduced in [2]—to D p is equivariant for small values of k and p. Mathematics Subject Classification (2000): 17B66, 16D99, 58J99.