Abstract

Let 𝒦 be the Lie superalgebra of contact vector fields on the supersymmetric line . We compute the action of 𝒦 on the modules of differential and pseudo-differential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols, 1-cohomology, and various uniserial subquotients of these modules. We also outline the computation of the 𝒦-equivalences and symmetries of their subquotients.