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

Abstract

Let ${\mathfrak{F}}_{ł}$ 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 ${\mathfrak{F}}_{ł}$ to ${\mathfrak{F}}_{\mu }$ 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.

This paper has been withdrawn by the author due to many errors