Conformally invariant quantization -- towards complete classification

2009/03/27 by Silhan, Josef
#17B56 (Secondary) #53A55 (Primary) 53A30 #58J70 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.4798

Abstract

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+δ]. Conformal quantization Q is a right inverse of the principle symbol map on D_w,w+δ such that Q is conformally invariant and exists for all w. This is known to exists for generic values of δ. We give explicit formulae for Q for all δ out of the set of critical weights. We provide a simple description of this set and conjecture its minimality.

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