2013/11/19 by Cai, Yan-an, Cheng, Yongsheng, Shen, Ran · 1 citation
#17B10 #17B65 #17B68 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1311.4855
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.