  The origin of the rather mysterious duality symmetry found in quantum
Liouville theory is investigated by considering the Liouville theory as the
reduction of a WZW-like theory in which the form of the potential for the
Cartan field is not fixed a priori. It is shown that in the classical theory
conformal invariance places no condition on the form of the potential, but the
conformal invariance of the classical reduction requires that it be an
exponential. In contrast, the quantum theory requires that, even before
reduction, the potential be a sum of two exponentials. The duality of these two
exponentials is the fore-runner of the Liouville duality. An interpretation for
the reflection symmetry found in quantum Liouville theory is also obtained
along similar lines.
