On massive higher spin supermultiplets in d=3

In this paper, using a frame-like gauge invariant formulation of the massive higher spin bosons and fermions, we develop a direct construction of the completely off-shell cubic vertices describing an interaction of the massless gravitino with the massive higher spin supermultiplets. To achieve the invariance under the local supersymmetry we introduce all necessary supertransformations (both for the physical as well as for the auxiliary fields) and thus all the supercurrents constructed are conserved on-shell. As an illustration of the technique used we present some lower superspin examples and then we consider the arbitrary superspin. We also check that the whole construction is completely consistent with all bosonic and fermionic gauge symmetries of the fields entering the supermultiplets.