I am reading this paper, in what says exactly:

"Weare dealing with a ray representation os the conformal group AND THEREFORE with a representation of the universal covering group of the conformal group"

And I do not underestand why having a ray representation (which I think is a projective representation) implies have a representation of the universal covering. Is this property general or just apply for the conformal group? How exactly is the representation of the universal cover in terms of the ray representation?

Thanks in advance.