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.

  • 1
    $\begingroup$ There is a general phenomenon behind this, see for example Bargmann's theorem. So you first lift your projective representation to a projective representation of the universal covering group (the lifting is done by the covering map). Then, because the universal cover is simply connected, you can apply Bargmann's theorem (to be able to do this there is a cohomological condition) to pass from projective representation to a usual linear representation. $\endgroup$
    – desos
    Nov 17, 2022 at 16:04


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