Discrete Series of Representations for the Modular Double of the Quantum Group Uq(sl(2, R))

The modular double of the 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 bar right arrow 1/tau. The use of the modular double in conformal field theory allows one to consider the region 1 < c < 25 for the central charge of the Virasoro algebra when vertical bar tau vertical bar = 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.