Unconstrained Massless Higher Spin Supermultiplet in AdS$_4$

We consider unconstrained formulation of the higher spin gauge theory in anti de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin supermultiplet in four-dimensional AdS$_4$. Such an irreducible supermultiplet $(\Phi_1, \Phi_2 \,; \Psi_1,\Psi_2)$ contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank $s= 0, 1, \ldots, \infty$), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin $s={\scriptstyle \frac{1}{2}}, {\scriptstyle \frac{3}{2}}, \ldots, \infty$).