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Simple Singular Whittaker Modules Over the Schrödinger Algebra

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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.

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, Jiangsu, People’s Republic of China

    Yan-an Cai

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yan-an Cai

  3. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China

    Xiufu Zhang

Authors
  1. Yan-an Cai
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  2. Xiufu Zhang
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Correspondence to Xiufu Zhang.

Additional information

Supported partially by the National Natural Science Foundation of China (Nos. 11571145, 11471333) and the General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M600140)

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Cai, Ya., Zhang, X. Simple Singular Whittaker Modules Over the Schrödinger Algebra. Commun. Math. Stat. 7, 475–483 (2019). https://doi.org/10.1007/s40304-019-00180-9

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  • DOI: https://doi.org/10.1007/s40304-019-00180-9

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