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.

中文翻译：

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Schrödinger代数上的简单奇异Whittaker模块

在大多数重要的代数上，没有简单的奇异的Whittaker模数，例如简单的复杂有限维李代数，仿射Kac–Moody Lie代数，Virasoro代数，Heisenberg-Virasoro代数和Schrödinger-Witt代数。但是，在本文中，我们在Schrödinger代数上构造了简单的奇异Whittaker模块。此外，对Schrödinger代数上的简单奇异Whittaker模块进行了分类。结果，在正部分上局部有限的Schrödinger代数的简单模块被完全分类。我们还给出了简单的最大重量模块和简单的奇特Whittaker模块的特性。