Quasi-Whittaker modules for the Schrodinger algebra

In this paper, we construct a class of new modules for the Schrodinger algebra S, called quasi-Whittaker modules. Different from [30], the quasi-Whittaker module is not induced by the Borel subalgebra of the Schrodinger algebra related with the triangular decomposition, but by its Heisenberg subalgebra H. We prove that, a simple S-module V is a quasi-Whittaker module if and only if V is a locally finite H-module. Furthermore, we classify simple quasi-Whittaker modules by central character of U(S) and their quasi-Whittaker functions. Finally, we characterize arbitrary quasi-Whittaker modules. (C) 2014 Elsevier Inc. All rights reserved.