644 research outputs found
Quasi-Whittaker modules for the Schr\"odinger algebra
In this paper, we construct a new class of modules for the Schr\"{o}dinger
algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the
quasi-Whittaker module is not induced by the Borel subalgebra of the
Schr\"{o}dinger algebra related with the triangular decomposition, but its
Heisenberg subalgebra \mH. We prove that, for a simple \mS-module ,
is a quasi-Whittaker module if and only if 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.Comment: 17 page
- …