Lagrangian description of the partially massless higher spin N=1 supermultiplets in $AdS_4$ space

In the recent paper [1] the classification of non-unitary representations of the three dimensional superconformal group has been constructed. From AdS/CFT they must correspond to N=1 supermultiplets containing partially massless fields in $AdS_4$. Moreover, the simplest example of such supermultiplets which contains a partially massless spin-2 was explicitly constructed. In this paper we extend this result and develop explicit Lagrangian construction of general N=1 supermultiplets containing partially massless fields with arbitrary superspin. We use the frame-like gauge invariant description of partially massless higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two partially massless bosonic and two partially massless fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the $AdS_4$ superalgebra is closed on-shell.