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Communications in Mathematics and Statistics

, Volume 7, Issue 4, pp 475–483 | Cite as

Simple Singular Whittaker Modules Over the Schrödinger Algebra

  • Yan-an Cai
  • Xiufu ZhangEmail author
Article
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Abstract

There are no simple singular Whittaker modules over most of important algebras, such as simple complex finite-dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, the Heisenberg–Virasoro algebra and the Schrödinger–Witt algebra. In this paper, however, we construct simple singular Whittaker modules over the Schrödinger algebra. Moreover, simple singular Whittaker modules over the Schrödinger algebra are classified. As a result, simple modules for the Schrödinger algebra which are locally finite over the positive part are completely classified. We also give characterizations of simple highest weight modules and simple singular Whittaker modules.

Keywords

Schrödinger algebra Highest weight modules Singular Whittaker modules Simple modules Locally finite modules 

Mathematics Subject Classification

17B10 17B20 17B66 17B70 

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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouPeople’s Republic of China
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouPeople’s Republic of China

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