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

Abstract

Modular double of quantum group U_q (sl(2)) with deformation parameter q=e^{iπτ} is a natural object explicitly taking into account the duality τ-> 1/τ. 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 |τ|=1. In this paper a new discrete series of representations for the modular double of U_q (sl(2,R)) is found for such τ.

8 pages, no figures