[en] In this paper, the question of existence of a natural and projectively equivariant symbol calculus is analysed
using the theory of projective Cartan connections. A close relationship is established between the existence of
such a natural symbol calculus and the existence of an sl(m+1,R)-equivariant calculus over R^m . Moreover,
it is shown that the formulae that hold in the non-critical situations over R^m for the sl(m+1,R)-equivariant
calculus can be directly generalized to an arbitrary manifold by simply replacing the partial derivatives by
invariant differentiations with respect to a Cartan connection.
Disciplines :
Mathematics
Author, co-author :
Mathonet, Pierre ; Université de Liège - ULiège > Département de mathématique > Département de mathématique
Radoux, Fabian ; Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
Cartan connections and natural and projectively equivariant quantizations
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