论文标题
Arthur的猜想和实际还原组的轨道方法
Arthur's Conjectures and the Orbit Method for Real Reductive Groups
论文作者
论文摘要
本文的前半部分是说明性的 - 我将在示例中审查Langlands分类的主要陈述以及Arthur对Adams，Barbasch和Vogan提出的实际还原群体的猜想。在下半年，我将注意力转向Orbit方法，Orbit方法是一种猜想的方案，用于对真正还原群体的不可还原统一表示分类。在组复杂的情况下，我将对轨道方法进行定义。主要的输入是在Arxiv：2108.03453中开发的一能理想和Harish-Chandra Bimodules的理论。我将证明我定义的轨道方法与Arthur的猜想通过自然双重性图有关。最后，我将为任意实际群体的这种轨道方法概括一下。
The first half of this article is expository -- I will review, with examples, the main statements of the Langlands classification and Arthur's conjectures for real reductive groups as formulated by Adams, Barbasch, and Vogan. In the second half, I will turn my attention to the Orbit Method, a conjectural scheme for classifying irreducible unitary representations of a real reductive group. I will give a definition of the Orbit Method in the case when the group is complex. The main input is the theory of unipotent ideals and Harish-Chandra bimodules, developed in arXiv:2108.03453. I will show that the Orbit Method I define is related to Arthur's conjectures via a natural duality map. Finally, I will sketch a possible generalization of this Orbit Method for arbitrary real groups.
