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We construct a range of supersymmetric cubic vertices for three masslesshigher spin supermultiplets in the four-dimensional space. We use frame-likemultispinor formalism, which allows to avoid most of the technical difficultiesand provides a uniform description for bosons and fermions. Our work is basedon the so-called Fradkin-Vasiliev formalism for construction of the cubicvertices, which requires the non-zero cosmological constant. Thus we firstconstruct the vertices in AdS space and then consider the flat limit. We showthat the AdS supersymmetric vertex is a sum of four elementary vertices forsupermultiplet components, while one of the vertices vanishes in the flat limitin agreement with the Metsaev's classification.

Cubic interaction vertices for massless higher spin supermultiplets in d=4