Abstract
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 U q ( sl 2 ) ( 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.
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