Discrete series of representations for the modular double of U_q(sl(2,R))

Modular double of quantum group U_q (sl(2)) with deformation parameter q=e^{i\pi\tau} is a natural object explicitly taking into account the duality \tau -> 1/\tau. The use of the modular double in CFT allows to consider the region 1<c<25 for the central charge of the Virasoro algebra when |\tau|=1. In this paper a new discrete series of representations for the modular double of U_q (sl(2,R)) is found for such \tau.