It is well-known that unitary irreducible representations for non-compact groups are generically infinite dimensional, leading to the principal series representations. We discuss how this enters for CFT correlators, and how it relates to the conventional OPE in terms of conformal primaries. We discuss next the case of CFT in Lorentzian signature where the principal series representation becomes even more robust. SYK-type models will be used to illustrate differences and similarities of principal series for CFT_1 under Euclidean and Minkowski treatments. In particular, we explain how the saturation of chaos bound can be understood as the strong coupling limit of Regge behavior where the leading Regge trajectory having an intercept at j=2.