The non-compact quantum dilogarithm and the Baxter equations

A review of tile recent formulation of the quantum discrete Liouville model in the strongly coupled regime (corresponding to the Virasoro central char ge 1 < c < 25) is presented. The Q-operator, describing the integrable stru cture of the model and satisfying a pair of dual Baxter equations. is obtai ned as a certain non-homogeneous transfer-matrix associated with the six-ve rtex model.