Whittaker modules for Uq(sl2)

We define and study the class of Whittaker modules for the quantum enveloping algebra Uq(sl2) of sl2. One of our main results describes an arbitrary Whittaker module as a quotient of Uq(sl2). From this description, we determine precise criteria for when a Whittaker module is simple as well as a decomposition of an arbitrary Whittaker module into indecomposable submodules. We also prove that the annihilator annUq(sl2)(V) of a Whittaker module V is generated by its intersection with the center of Uq(sl2). This is the analogue of a classical result in the Lie algebra setting due to Kostant.