Tensors and spinors in de Sitter space

We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ a coordinate index free formalism using $d+2$ dimensional ambient space. expand embedding space to cover spinor tensor fields any even or odd dimension. Our goal is furnish self-contained toolkit study of arbitrary spin de Sitter, with applications cosmological perturbation theory. The construction spinors shown extensive detail. Concise expressions action isometry generators on generic bulk fields, 2-point spinors, derivation uplift spinorial covariant derivative are included.