frame as it already exists for unflowed vertex operators, its occurrence being necessary in order to properly normalize spectral flowed states in the $x$-basis. Our strategy for determining this singular term relies on a generalization of the reflection symmetry in sectors with $\omega\ne 0$, since a single reflection in a two-point function should switch the corresponding regular and contact terms.

Reflection in the Euclidean model is a Weyl-type symmetry expressing the unitary equivalence of certain irreducible representations of SL($2,\mathbb C$) and the affine modules constructed upon them. In the Lorentzian case, in the $m$-basis, this interpretation is retained for the family of continuous series, since the generalized reflection symmetry intertwines between the corresponding affine modules and their spectrally flowed images. In the space-time picture as well as for discrete representations in $m$-basis and their related modules, reflection is recognized as a $\mathbb Z_2$ symmetry relating microscopic states in the sense of [@Teschner:1999ug].

The final expression we get for the two-point function deserves a couple of comments. Of course, it reduces to the known propagator in the unflowed limit, [*i.e.*]{} $\omega \rightarrow 0$. On the other hand, its dependence on the worldsheet coordinates consistently shows that, although they retain some conformal 