Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models

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 6= 0 and isospin values of the type J = j − j(k + 2), 2j, 2j ∈ ZZ+. CERN-TH.6289/91 December 1991 CERN-TH.6289/91 SISSA 120/FM/91 0∗ Permanent address: Institute for Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria e-mail: mvxtst::furlan, ganchev@itssissa, paunov@itssissa, petkova@itssissa