论文标题
本地theta通信：基本理论
Local theta correspondence: the basic theory
论文作者
论文摘要
我们对经典不变理论及其现代扩展“超越古典理论”进行了基础介绍，通常称为局部theta对应理论。我们解释了该理论的两个基本断言：二重性猜想和Kudla-Rallis保护关系猜想。我们提供了有关用Langlands-Vogan参数明确描述本地Theta对应的问题的状态报告。我们在讨论某个自动连续性问题的讨论中结束，该问题在代数和平滑的环境中表现出理论的统一性。
We give an elementary introduction to Classical Invariant Theory and its modern extension "Transcending Classical Invariant Theory", commonly known as the theory of local theta correspondence. We explain the two fundamental assertions of the theory: the Howe duality conjecture and the Kudla-Rallis conservation relation conjecture. We give a status report on the problem of explicitly describing local theta correspondence in terms of Langlands-Vogan parameters. We conclude with a discussion on a certain problem of automatic continuity, which manifests unity of the theory in algebraic and smooth settings.
