Whittaker modules and quasi-Whittaker modules for the Schrödinger algebra in (2 + 1)-dimensional spacetime

Abstract

In this paper, we classify simple (quasi)-Whittaker modules for the Schrödinger Lie algebra s2 in (2+1)-dimensional space-time. Moreover, we show that a simple sn-module is a Whittaker module if and only if it is a locally finite sn+-module, and it is a quasi-Whittaker module if and only if it is a locally finite hn-module. Also, we determine the center of U(s2) and U(s2/Cz).