A class of non-weight modules of Uq(sl2) and Clebsch-Gordan type formulas

In this paper, we construct a class of new modules for the quantum group U-q(sl(2)) which are free of rank 1 when restricted to C[K-+/- 1]. The irreducibility of these modules and submodule structure for reducible ones are determined. It is proved that any C[K-+/- 1]-free U-q(sl(2))-module of rank 1 is isomorphic to one of the modules we constructed, and their isomorphism classes are obtained. We also investigate the tensor products of the C[K-+/- 1]-free modules with finite-dimensional simple modules over U-q(sl(2)), and for the generic cases, we obtain direct sum decomposition formulas for them, which are similar to the well-known Clebsch-Gordan formula for tensor products between finite-dimensional weight modules over U-q(sl(2)).