methods employed in [@BB].

We show in Lemma \[neighborhood\] that there exists a wedge $W_0 \in \Ws$ such that $\lambda W_0 \subset W_R$ for all $\lambda$ in a neighborhood of the identity in ${\mbox{SO$_0(2,n\!-\!1)$}}$. Therefore, for any $j = 2,\ldots,n-1$ one has $\lambda_{0 j} (s) \, W_0 \subset W_R$ for the boosts $\lambda_{0 j} (s)$ in the $0$–$j$–plane for all sufficiently small parameters $s$. From equation (\[010j\]) in Appendix \[grouptheory\] we have $$e^{\, itM_{0 1}} e^{\, isM_{0 j}} = 
e^{\, is(\cosh(t)M_{0 j} + \sinh(t) M_{1 j})}  e^{\, itM_{0 1}} \, .$$ Thus we get for any vector $\Phi \in {{\cal H}}$ and operator $A^* \in {{\cal A}}(W_0)$ $$\label{equation11}
\langle \Phi , \, e^{\, itM_{0 1}} 
\, e^{\, isM_{0 j}} A^* e^{\, -isM_{0 j}}  {{\Omega \rangle}}=  \langle \Phi , \, 
e^{\, is(\cosh(t)M_{0 j} + \sinh(t) M_{1 j})}\,  e^{\, itM_{0 1}} 
A^* {{\Omega \rangle}}\, .$$ We are now in the position of employing the argument given in [@AdS] to yield the equalities $$\label{equation13}
J_{W_R}  e^{\, isM_{0 j}}   =   
e^{\, is(\cos(\beta/2) M_{0 j} + i \sin(\beta/2) M_{1 j})} J_{W_R} \, .$$ As pointed out in [@AdS], the operator on the left–hand side of this equation is anti–unitary, which entails that $\beta$ is an 