Conformally invariant quantization - towards the complete classification

Let M be a smooth manifold equipped with a conformal structure, E[w] the space of densities with the conformal weight w and Dw,w+δ the space of differential operators from E[w] to E[w+δ]. Conformal quantization Q is a right inverse of the principle symbol map on Dw,w+δ such that Q is conformally invariant and exists for all w. There are partial results concerning the dependence on δ: the existence of Q is known for generic values of δ∈R and the nonexistence is known for a set of critical weights δ∈Σ⊆R. We complete these results, i.e. we show that Q exists for all noncritical weights δ∉Σ. We give explicit formulae for Q for all such δ in terms of the conformal tractor calculus.