A general BRST-BV Lagrangian for arbitrary-spin free fields in AdS is constructed by reducing the problem to solving algebraic defining equations for spin operators.
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N=2 abelian higher-spin cubic (s1,s2,s2) vertices have analytic structure fully fixed by the supercurrents J++_{\alpha(s-1)\dot{\alpha}(s-1)}, J^+_{\alpha(s-1)\dot{\alpha}(s-2)} and \bar J^+_{\alpha(s-2)\dot{\alpha}(s-1)} for s1 \ge 2 s2.
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Structure of $\mathcal{N} = 2$ superfield higher-spin abelian cubic interactions
N=2 abelian higher-spin cubic (s1,s2,s2) vertices have analytic structure fully fixed by the supercurrents J++_{\alpha(s-1)\dot{\alpha}(s-1)}, J^+_{\alpha(s-1)\dot{\alpha}(s-2)} and \bar J^+_{\alpha(s-2)\dot{\alpha}(s-1)} for s1 \ge 2 s2.