We are interested in the study of the space of $n$-ary differential operators denoted by $\mathfrak{ D}_{ \underline{ \l},\mu}$ where $\underline{ \l}=(\l_{ 1},...,\l_{ n})$ acting on weighted densities from $\frak F_{ \l_1}\otimes\frak F_{ \l_2}\otimes...\otimes\frak F_{ \l_n}$ to $\frak F_{ \mu}$ 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 $\mathfrak{ D}_{ \underline{ \lambda},\mu}^k$ to the corresponding space of symbols as well for the explicit expression of the associated quantization map.
Categories: math.DG