Whittaker modules for

We define and study the class of Whittaker modules for the quantum enveloping algebra of . One of our main results describes an arbitrary Whittaker module as a quotient of . 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 of a Whittaker module V is generated by its intersection with the center of . This is the analogue of a classical result in the Lie algebra setting due to Kostant.