Whittaker modules for Uq(sl2)

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.  2005 Elsevier Inc. All rights reserved.