The binary aff(n|1)-invariant differential operators on weighted densities on the superspace R1|n and aff(n|1)-relative cohomology

We consider the aff(n|1)−module structure on the spaces of differential bilinear operators acting on the superspaces of weighted densities. We classify aff(n|1)−invariant binary differential operators acting on the spaces of weighted densities. This result allows us to compute the first aff(n|1)−relative differential cohomology of K(n) with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities.