Conformally invariant quantization -- towards complete classification

Details Conformally invariant quantization -- towards complete classification Conformally invariant quantization -- towards complete classification

2009-03-27

arxiv.org/abs/0903.4798v1

Mathematics

Differential Geometry

18 pages

Scientific paper

Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$ is a right inverse of the principle symbol map on $D_{w,w+\delta}$ such that $Q$ is conformally invariant and exists for all $w$. This is known to exists for generic values of $\delta$. We give explicit formulae for $Q$ for all $\delta$ out of the set of critical weights. We provide a simple description of this set and conjecture its minimality.

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