Cyclic Quantum Dilogarithm and Shift Operator
  {}From the cyclic quantum dilogarithm the shift operator is constructed with $q$ is a root of unit and the representation is given for the current algebra introduced by Faddeev $et ~al$. It is shown that the theta-function is factorizable also in this case by using the star-square equation of the Baxter-Bazhanov model. 
Zhan-Ning Hu and Bo-Yu Hou