Publication details

Conformally invariant quantization – towards the complete classification.



Year of publication 2014
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

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