Free massless fields of arbitrary spin in the de Sitter space and initial data for a higher spin superalgebra

Linearized curvatures are constructed for massless higher spin fields on the (anti-) de Sitter background. The quite uniform description for free massless fields of all integer and half-integer spins s ≥ 3/2 is presented, based on these curvatures. In particular, the actions and the equations of motion are given in a simple form. The proposed linearized curvatures provide 'initial data' for determination of a non-Abelian higher spin symmetry that may correspond to a hypothetical non-trivial theory of higher spins interacting with gravity and themselves. It is noted that the conjugation law for fermion fields should be modified drastically after transition from the anti-de-Sitter geometry to the de Sitter one. (author)