  The quantisation of the Wess-Zumino-Witten model on a circle is discussed in
the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex
operators is described by an exchange relation with a braiding matrix, $Q$.
Using quantum consistency conditions, the braiding matrix is found explicitly
in the fundamental representation. This matrix is shown to be related to the
Racah matrix for $U_t(SL(N))$. From calculating the four-point functions with
the Knizhnik-Zamolodchikov equations, the deformation parameter $t$ is shown to
be $t=\exp({i\pi /(k+N)})$ when the level $k\ge 2$. For $k=1$, there are two
possible types of braiding, $t=\exp({i\pi /(1+N)})$ or $t=\exp(i\pi)$. In the
latter case, the chiral vertex operators are constructed explicitly by
extending the free field realisation a la Frenkel-Kac and Segal. This
construction gives an explicit description of how to chirally factorise the
$SU(N)_{k=1}$ WZW model.
