Quasi-Whittaker modules for the Schrödinger algebra

Abstract

In this paper, we construct a new class of modules for the Schrödinger algebra $\mS$, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schrödinger algebra related with the triangular decomposition, but its Heisenberg subalgebra $\mH$. We prove that, for a simple $\mS$-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite $\mH$-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in $U(\mS)$ and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.

17 pages

References in corpus (3)

• Irreducible representations of untwisted affine Kac-Moody algebras
• Simple Virasoro modules which are locally finite over a positive part
• On simple modules over conformal Galilei algebras