Abstract
The possibility of strong coupling quantum Liouville garvity is investigated via infinite dimensional representations of U q s l(2, C) with q at a root of unity. It is explicitly shown that the vertex operator in this model can be written by a tensor product of a vertex operator of the classical Liouville theory and that of weak coupling quantum Liouville theory. Some discussions about the strong coupling Liouville gravity within this formulation are given.
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