of $J_{W_R}$ and clarify its relation to spacetime reflections. Plugging $\beta = 2 \pi$ into equation (\[equation13\]), we see that for small $s$ $$J_{W_R}  e^{\, isM_{0 j}}   =   
e^{\, - is  M_{0 j}} J_{W_R} \, , \quad j = 2,\ldots,n-1 \, .$$ This relation can be extended to arbitrary $s$ by iteration, if one decomposes $e^{\, isM_{0 j}}$ into an $m$–fold product $(e^{\, i(s/m)M_{0 j}})^m$ for sufficiently large $m$. A similar argument with $\lambda_{0j}$ replaced by $\lambda_{0n}$ and equation (\[010j\]) replaced by (\[010n\]) yields $$\label{WR0n}
J_{W_R}  e^{\, isM_{0 n}}   =   
e^{\, - is  M_{0 n}} J_{W_R} \, .$$ On the other hand, modular theory yields $$J_{W_R}  e^{\, isM_{0 1}}   =   
e^{\, is  M_{0 1}} J_{W_R} \, .$$ Since these one-parameter subgroups generate ${\mbox{SO$_0(2,n\!-\!1)$}}$, the intertwining properties of $J_{W_R}$ with all unitaries $U(\lambda) \in U({\mbox{SO$_0(2,n\!-\!1)$}})$ are determined.

\[TCPgroup\] Given Standing Assumptions (i)–(iv), one has $$J_{W_R} U(\lambda)  =  U(\theta_{01}\lambda\theta_{01}) J_{W_R} \, ,$$ for all $\lambda \in {\mbox{SO$_0(2,n\!-\!1)$}}$, where $\theta_{01} = \diag(-1,-1,1,\ldots,1)$ is the reflection which changes the sign of the $0$–$1$–coordinates of the points in (the reflection about the edge of the wedge $W_R$).

Hence, if we define $U(\theta_{01}\lambda) \doteq J_{W_R}U(\lambda)$, for any $\lambda \in {\mbox{SO$_0(2,n\!-\!1)$}}$, the following partial analogue of the 