Harish-Chandra模的光滑Frechet整体化

Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules

In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra A(G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and A(G) and which embeds as the space of analytic vectors in all Banach globalizations of V.

Dependence on parameters of CW globalizations of families of Harish-Chandra modules and the meromorphic continuation of $C^{\infty}$ Eisenstein series

The first main result is that the Casselman-Wallach Globalization of a real analytic family of Harish-Chandra modules is continuous in the parameter. Our proof of this result uses results from the thesis of Vincent van der Noort in several critical ways. In his thesis the holomorphic version of the result was proved in the case when the parameter space is a one dimensional complex manifold up to a branched covering. The second main result is a proof of the meromorphic continuation of $C^{\infty}$ Eisenstein series.using Langlands' results in the $K$ finite case as an application of the methods…

一类Harish-Chandra模的光滑整体化的上同调性质

Cohomological properties of the smooth globalization of a Harish-Chandra module

证明了系数为实秩1的半单李群中无挠格的上同调在Harish-Chandra模的分布向量整体化中的有限性.上同调用自守形式和尖点形式表示。我们还考虑了这些全球化的幂零部分的岩泽分解的组的李代数上同调。

Harish-Chandra与Whittaker普兰歇尔定理的希尔伯特和弗雷歇丛版本

Hilbert and Fréchet bundle versions of the Harish-Chandra and Whittaker Plancherel Theorems

本文聚焦缓增对偶空间上的希尔伯特与弗雷歇向量丛，以表示论方法完整证明Whittaker普兰歇尔定理的直积分版本，无需艾森斯坦积分与抽象理论。

Fréchet globalisations of Harish-Chandra supermodules

For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of the Casselman-Wallach globalisation theorem: There is an equivalence between the category of Harish-Chandra modules and the category of SF-representations (smooth Fréchet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general general form of the Gel'fand-Kazhdan criterion due to Sun-Zhu.

扭曲 $\mathcal D$-模族与 Harish-Chandra 模的算术模型

Families of twisted $\mathcal D$-modules and arithmetic models of Harish-Chandra modules

本文发展了一般基概形上的扭曲 $\mathcal D$-模理论及闭 $K$-轨道形式理论，并利用它们几何构造了上同调诱导模的半整模型，进而证明了其投射性和无挠相对李代数上同调等算术良好性质。