Lagrangian formulation of free arbitrary N-extended massless higher spin supermultiplets in 4D, AdS space

We derive the component Lagrangian for the free $N$-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction is based on frame-like description of massless integer and half-integer higher spin fields. The massless supermultiplets are formulated for $N\leq 4k,$ where $k$ is a maximal integer or half-integer spin in the multiplet. The supertransformations that leave the Lagrangian invariant are found and it is shown that their algebra is closed on-shell.