On Higher Spin Symmetries in AdS_{5}

Understand

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.