Whittaker modules for Uq (sl2)

We define and study the class of Whittaker modules for the quantum enveloping algebra U-q (sl(2)) Of sl(2). One of our main results describes an arbitrary Whittaker module as a quotient of U-q (sl(2)). 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 ann(Uq(sl2))(V) of a Whittaker module V is generated by its intersection with the center of U-q(sl(2)). This is the analogue of a classical result in the Lie algebra setting due to Kostant. (c) 2005 Elsevier Inc. All rights reserved.