Symetries of modules of differential operators on $S^{1|1}$

Abstract: Let $\frak F_{\l}$ be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the space $\mathfrak{D}{\lambda,\mu}^k$ of k-th order linear differential operators from $\frak F{\l}$ to $\frak F_{\mu}$ as $\mathfrak{osp}(1|2)$-module and we determine the space $\mathfrak{I}{\lambda,\mu}^k$ of linear maps on $\mathfrak{D}{\lambda,\mu}^k$ commuting with the $\mathfrak{osp}(1|2)$-action.