Conformally invariant quantization – towards the complete classification.
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Differential Geometry and its Applications |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.sciencedirect.com/science/article/pii/S0926224513001046 |
| Doi | http://dx.doi.org/10.1016/j.difgeo.2013.10.016 |
| 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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