  In the spirit of the quantum Hamiltonian reduction we establish a relation
between the chiral $n$-point functions, as well as the equations governing
them, of the $A_1^{(1)}$ WZNW conformal theory and the corresponding Virasoro
minimal models. The WZNW correlators are described as solutions of the Knizhnik
- Zamolodchikov equations with rational levels and isospins. The technical tool
exploited are certain relations in twisted cohomology. The results extend to
arbitrary level $k+2 \neq 0$ and isospin values of the type $J=j-j'(k+2)$, $ \
2j, 2j' \in Z\!\!\!Z_+$.
