论文标题
诺伊曼（Neumann
A Stone-von Neumann equivalence of categories for smooth representations of the Heisenberg group
论文作者
论文摘要
经典的石像Neuman定理将Heisenberg Group $ h_n $的不可约合的统一表示与其中心$ Z $的非平凡的统一角色联系起来，并在构建Metapspoctic Group的振荡器表示中起着至关重要的作用。 在本文中，我们将这些想法扩展到了非独立和不可否定的表示形式，从而在$ z $的某些表示形式和$ h_n $的某些表示之间获得了等效性。我们的主要结果是平稳的等效性，它涉及杜克洛克斯（Du Cloux）对纳什组的可区分表示和平稳的不可限制系统的基本思想。我们展示了如何将振荡器表示形式扩展到平滑设置，并为退化的Whittaker模型提供了应用程序以进行还原组的表示。 我们还包括一个代数等效性，可以将其视为对喀西瓦拉的引理的概括。
The classical Stone-von Neuman theorem relates the irreducible unitary representations of the Heisenberg group $H_n$ to non-trivial unitary characters of its center $Z$, and plays a crucial role in the construction of the oscillator representation for the metaplectic group. In this paper we extend these ideas to non-unitary and non-irreducible representations, thereby obtaining an equivalence of categories between certain representations of $Z$ and those of $H_n$. Our main result is a smooth equivalence, which involves the fundamental ideas of du Cloux on differentiable representations and smooth imprimitivity systems for Nash groups. We show how to extend the oscillator representation to the smooth setting and give an application to degenerate Whittaker models for representations of reductive groups. We also include an algebraic equivalence, which can be regarded as a generalization of Kashiwara's lemma from the theory of $D$-modules.
