  We construct unitary irreducible representation of the de Sitter group, that
forms the basis for the study of $dS_{d+1}$ QFT. Using the intertwining kernel
analysis, we discuss bosonic symmetric tensor, and fermionic higher-spinors.
Particular care is given to the structure and construction of exceptional
series and fermionic operators. We discuss the discrete series, and explain how
and why the exceptional series give rise to seemingly non-invariant correlators
in de Sitter. Using tools from Clifford analysis, we show that for $d>3$, there
are no exceptional fermionic representations, and so no unitary
(higher)-gravitino fields. We also consider the structure of representations
for $d=3$ and $d=2$, as relevant for the study of $dS_4$, the only space
allowing for unitary gravitino and its generalisation, and of $dS_3$.
