Let $\mathrm{SO}(1,d-1)^\uparrow$ be the connected Lorentz group in $d$ dimensions. I am looking for a book/article where its finite-dimensional projective representations are studied in detail. Rather surprisingly, I haven't been able to find anything online, so here I am.
Some topics that I'd like to see discussed in the references are:
Does any projective representation correspond to a regular representation of the spin group $\mathrm{Spin}(1,d-1)$?
Is any projective representation decomposable (i.e., it can be written, up to similarity, as the direct sum of irreducible representations)?
How can we classify all irreducible representations? in other words, how many labels do we need in order to specify a particular representation? are they half-integers? (in $d=4$, we have two labels, cf. the $(m,n)$ representation, which is $(2m+1)(2n+1)$-dimensional)
Can an arbitrary object transforming according to an irreducible representation be written as the tensor product of spinors? (in $d=4$, an element transforming according to the $(m,n)$ representation can be identified with an object carrying $m$ dotted and $n$ un-dotted spinor indices).
How does a large transformation ($C,P,T$) act on an arbitrary object transforming under a particular projective representation? (in $d=4$, the general formulas can be found e.g. in Wightman's PCT).
Any reference that addresses at least one of these topics will be welcome and appreciated. Ideally, the best reference would discuss all of them.
I think I know the answer for the first and second sub-questions, but I've included them anyway for completeness (the lack of results in the typical google searches suggests me that this post might end up being the first result when one googles "representations of the Lorentz in higher dimensions").