  Starting from Sklyanin's separation of variables for the sl3 Yangian model,
we derive the separation of variables for the quantum sl3 Gaudin model. We use
the resulting new variables for rewriting the sl3 Knizhnik-Zamolodchikov
equations, and comparing them with certain null-vector equations in conformal
field theories with W3-algebra symmetry. The two sets of equations are
remarkably similar, but become identical only in the critical level limit. This
is in contrast to the sl2 Knizhnik-Zamolodchikov equations, which are known to
be equivalent to Belavin-Polyakov-Zamolodchikov equations for all values of the
level.
