One point about Wick rotation is puzzling me and I can not find explanations in books. It concerns the invariants formed from scalar product and solutions to equation. So I will expose my way of reasoning to let you see if it is correct and at the end ask more specific questions.
Let's start...
In another reference (I forgot which ones precisely, but it cites the one you are talking about) I read that in fact it's not very important which U(1) ones factorizes since one can always take linear combinations.
Your reference is really perfect, thank you! In fact, the Sohnius review...
Exact, you are right, I have the book but I did not recognize since the notations differs from the usual ones. Sadly the construction is not fully explained, and I don't have access to the original paper from Hagg, Lopuszanski, Sohnius.
Do you know somewhere else where this construction is...
In fact, we can always decompose as U(N) = U(1) x SU(N), where the U(1) is the usual symmetry associated to the R-charge for N=1, except for N=4 where the R-operator vanishes, and we get only SU(4).
I took a look at the paper you said, and the U(1)_Z group which he speaks about is not the same...
Last year I was studying supersymmetry and since them I'm regularly thinking to one question for which I don't have answer: when one looks at the susy algebra with N generators, one sees that there is a U(N) R-symmetry. But for N=4, the group is in fact SU(4).
To explain this, one generally...