Abstract :
[en] The existence of a natural and projectively equivariant quantization in the
sense of Lecomte was proved recently by M. Bordemann,
using the framework of Thomas-Whitehead connections. We give a new proof of
existence using the notion of Cartan projective connections and we obtain
an explicit formula in terms of these connections. Our method yields the
existence of a projectively equivariant quantization if and only if an
sl(m+1,R)-equivariant quantization exists in the flat situation, thus solving one of
the problems left open by M. Bordemann.
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