Whittaker modules and quasi-Whittaker modules for the Euclidean Lie algebra [formula omitted

Abstract

In this paper, we classify simple Whittaker modules and simple quasi-Whittaker modules for the Euclidean Lie algebra E=e(3). We show that a simple e(3)-module is a Whittaker module if and only if it is a locally finite E+-module, and it is a quasi-Whittaker module if and only if it is a locally finite P-module. In particular, we get a class of simple weight e(3)-modules which have infinite-dimensional weight spaces.