  Conformal Field Theory in a Minkowski setting is discussed in an embedding
space approach, paying special attention to causality constraints for
four-point amplitudes. The physics of dilatation and Lorentz boost is
emphasized in specifying the non-compact Maximal Abelian subgroup (MASG) of
$SO(d,2)$. Reduction of a Conformal Field Theory (CFT) four-point amplitudes as
functions of cross ratios is shown to be equivalent to enforcing $H$
bi-invariance, i.e., $F(hgh')=F(g)$, with $g\in SO(d,2)$ and $H$ an appropriate
subgroup. Causality is imposed by introducing appropriate semigroups. Causal
zonal spherical functions are constructed, making contact with Minkowski
conformal blocks introduced previously.
