Simple Schrödinger modules which are locally finite over the positive part

Xiufu Zhang ^[1] ; Yongsheng Cheng ^[2]
1. [1] Jiangsu Normal University
  
  Jiangsu Normal University
  
  China
2. [2] Henan University
  
  Henan University
  
  China
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 7 (July 2015), 2015, págs. 2799-2815
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.09.029
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Resumen
- It is proved that a simple module which is locally finite over the positive part of the Cartan decomposition for a finite-dimensional Lie algebra with triangular decomposition and solvable positive part is a highest weight module, a Whittaker module or a singular Whittaker module. The classification of simple highest weight modules for the Schrödinger algebra follows from the classification of all simple lowest weight module for the Schrödinger algebra given by Dobrev, Doebner and Mrugalla. The simple Whittaker modules for the Schrödinger algebra are classified in this paper. The singular Whittaker vectors for the universal singular Whittaker module are given.