Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities
We are interested in the study of the space of $n$-ary differential operators denoted by $\mathfrak{D}_{\underlineł,μ}$ where $\underlineł=(ł_{1},...,ł_{n})$ acting on weighted densities from $\frak F_{ł_1}\otimes\frak F_{ł_2}\otimes...\otimes\frak F_{ł_n}$ to $\frak F_μ$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. As a consequence, we prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathfrak{D}_{\underlineλ,μ}^k$ to the corresponding space of symbols as well for the explicit expression of the associated quantization map.
math.DG↗