One of the most interesting problems in representation theory is the study of the unitarity of principal series of split real reductive groups. When the group is linear and the principal series is spherical, the problem is fairly well understood, but the general case is still "mysterious".
In this talk we focus on one particular non-linear group G, the double cover of the split F4, and attempt to describe its complementary series. The key tool is a method to relate the intertwining operator for non spherical principal series of G to the intertwining operator for spherical principal series of some linear groups. This method gives non-unitarity certificates and provides a good insight in the unitary dual of G.