  Our main goal here is to provide an introduction on some of the well
established properties of the representation theory of SO(d+1,1), for those
considering to think on physical problems set in de Sitter space in terms of
these representations. With this purpose we review two intertwining maps, the
map G that is used in constructing a well defined inner product for the
complementary series representations and the map Q that is involved in
constructing composite representations. We give explicit examples from the
late-time boundary of de Sitter on the practical use of the complementary
series inner product and in building a tensor product representation from
unitary principal series irreducible representations.
