We consider in detail the structure of quartic vertices for massless higher spin fields on Minkowski background, and study the consistency conditions imposed on cubic and quartic interactions by symmetries of the S-matrix. We discuss the possibility of generalizing the construction of quartic vertices to -dimensional anti-de Sitter space.
Dempster, P., & TSULAIA, M. (2012). On the structure of quartic vertices for massless higher spin fields on Minkowski background. Nuclear Physics, Section B, 865(2), 353-375. https://doi.org/10.1016/j.nuclphysb.2012.07.031