zero-mode algebra must be enhanced to avoid a coupling independent restriction on the masses of physical states and to give account of long string configurations, [*i.e.*]{} finite energy states classically corresponding to strings stretched close to the boundary of AdS$_3$ [@Maldacena:1998bw; @Maldacena:1998uz; @Seiberg:1999xz].

The key ingredient for generating the full physical spectrum is the [*spectral flow*]{} [@Maldacena:2000hw; @Maldacena:2000kv; @Maldacena:2001km; @Israel:2003ry], a family of automorphisms of the current algebra, labelled by an integer number $\omega$, the so-called spectral flow number or charge, which, in some cases, can be recognized as the amount of winding of a long string along the angular direction of AdS$_3$. For a rational WZNW model, spectral flow trivializes, as it relates standard representations, mapping primary states of one into the current algebra descendants of another. In the SL($2,\mathbb R$)-WZNW model, a Lorentzian non-rational CFT, modules with different spectral flow charges turn out to be generically non-equivalent, spectral flow automorphisms thus defining new representations. Operators with non-trivial spectral flow describing the *winding sector* of the theory were shown to play an important role in the models described above.

Correlators involving only spectrally unflowed vertex operators are obtained from the correlation functions in the H$_3^+$-WZNW model [@Teschner:1997ft; @Teschner:1999ug], the 