Whittaker Modules Over Some Generalized Weyl Algebras

Abstract

In Benkart and Ondrus (Represent. Theory 13, 141–164 2009), Benkart and Ondrus investigated Whittaker modules for generalized Weyl algebras. Following the results of Benkart and Ondrus, we study Whittaker modules for three special kinds of generalized Weyl algebras in this note, including Rueda’s algebras, the algebras U_q(f(K)) and U_q(f(K,H)). In particular, we acquire the centers of the last two classes of algebras before giving an explicit description of their simple Whittaker modules.