LIOUVILLE THEORY AND SPECIAL COADJOINT VIRASORO ORBITS

We describe the Hamiltonian reduction of the coadjoint Kac-Moody orbit s to the Virasoro coadjoint orbits explicitly in terms of the Lagrangi an approach for the Wess-Zumino-Novikov-Witten theory. While a relatio n of the coadjoint Virasoro orbit Diff S-1/SL(2, R) to the Liouville t heory has already been studied, we analyze the role of special coadjoi nt Virasoro orbits Diff S-1/(T) over tilde(+/-,n), corresponding to st abilizers generated by the vector fields with double zeros. The orbits with stabilizers with single zeros do not appear in the model. We fin d an interpretation of zeros x(i) of the vector field of stabilizer (T ) over tilde(+/-,n) and additional parameters q(i);, i = 1,..., n, in terms of quantum mechanics for n-point particles on the circle. We arg ue that the special orbits are generated by insertions of ''wrong sign '' Liouville exponential into the path integral. The additional parmet ers q(i) are naturally interpreted as accessory parameters for the uni formization map. Summing up the contributions of the special Virasoro orbits we get the integrable sinh-Gordon type theory.