On Higher Spin Symmetries in AdS_{5}

Abstract: A special embedding of the SU(4) algebra in SU(10), including both spin two and spin three symmetry generators, is constructed. A possible five dimensional action for massless spin two and three fields with cubic interaction is constructed. The connection with the previously investigated higher spin theories in $AdS_{5}$ background is discussed. Generalization to the more general case of symmetries, including spins $2,3,\dots s$, is shown.