Modules of bilinear differential operators over the orthosymplectic superalgebra \(\mathfrak{osp}(1|2)\) (Q1669195)

Recently, several papers deal with the problem of equivariant quantization in the context of supergeometry and the motivation in this work is the extension of some previous results to the binary case. More precisely, the authors consider the superspace of bilinear differential operators from the space of tensor densities on the supercircle \(S^{1|1}\). The analogue in the super setting, of the projective algebra \(sl(2)\), is the orthosymplectic Lie superalgebra \(\mathfrak{osp}(1|2)\). The main result is theorem 4 which proves the existence of an isomorphism between two \(\mathfrak{osp}(1|2)\)-modules. This isomorphism, called \textit{conformally equivariant symbol map}, is unique for a fixed principal symbol.