  The operator realizing a Dehn twist in quantum Teichmuller theory is
diagonalized and continuous spectrum is obtained. This result is in agreement
with the expected spectrum of conformal weights in quantum Liouville theory at
c>1. The completeness condition of the eigenvectors includes the integration
measure which appeared in the representation theoretic approach to quantum
Liouville theory by Ponsot and Teschner. The underlying quantum group structure
is also revealed.
