  We continue to study minimal Liouville gravity (MLG) using a dual approach
based on the idea that the MLG partition function is related to the tau
function of the A_q integrable hierarchy via the resonance transformations,
which are in turn fixed by conformal selection rules. One of the main problems
in this approach is to choose the solution of the Douglas string equation that
is relevant for MLG. The appropriate solution was recently found using
connection with the Frobenius manifolds. We use this solution to investigate
three- and four-point correlators in the unitary MLG models. We find an
agreement with the results of the original approach in the region of the
parameters where both methods are applicable. In addition, we find that only
part of the selection rules can be satisfied using the resonance
transformations. The physical meaning of the nonzero correlators, which before
coupling to Liouville gravity are forbidden by the selection rules, and also
the modification of the dual formulation that takes this effect into account
remains to be found.
