A primary field that is characterized by the conformal dimension Δ Δ and representation ρ ρ behaves as a highest-weight vector in an induced representation of the conformal group from the subgroup generated by dilations and rotations. In particular, the conformal dimension Δ Δ characterizes a representation of the subgroup of dilations. In two dimensions, the fact that this induced representation is a Verma module appears throughout the literature. For higher-dimensional CFTs (in which the maximally compact subalgebra is larger than the Cartan subalgebra), it has recently been appreciated that this representation is a parabolic or generalized Verma module.