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$\DeclareMathOperator\SO{SO}$For $n\geq 2$, the $n$-dimensional connected Lorentz group is defined as $$\SO(n-1,1)^{\uparrow}=\{f\in M_n (\mathbb{R}):f^T\eta f=\eta, \det (f)=1,f^0_0>0\}$$ where $$...

Let $G$ be a connected Lie group with universal cover $\tilde{G}$. I would really appreciate if someone could give me a reference for the proof of the following fact: "Every projective unitary ...