Atlas of Lie Groups

李群图集

• 批准号: 0532393
• 负责人: Jeffrey Adams
• 金额: --
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532393&HistoricalAwards=false
• 关键词: Atlas; Lie; Groups

The problem of computing the set of irreducible unitary representations ofa Lie group is one of the main unsolved problems in representation theory.There are two primary goals of this proposal.The first goal is to compute the unitary dual of real and p-adic Lie groups,by a combination of mathematical and computational techniques. In particularwe plan to develop a set of software packages for computing structure theory ofLie groups and unitary representations.The impact of the project is addressed by our second goal, which is to makeinformation about Lie groups and representation theory accessible to the generalmathematical audience. This will be done through a web site which will containinteractive tools for accessing data about Lie groups and representations. Thesoftware we will develop will be publicly available, and provided with extensivedocumentation and a well designed user interface.The project will also have an impact on education by providing a mechanismfor new researchers to learn about the field and make contributions to it. In ad-dition, it will generate many mathematical and computational problems whichwill be tractable to non-experts, and will centralize and organize the state ofthe field to make it more accessible.We hope this project will have as much or more of an impact in Lie theoryas the Atlas of Finite Groups has in finite group theory.

李群的不可约酉表示集的计算问题是表示理论中尚未解决的主要问题之一。这项提议有两个主要目标。第一个目标是通过结合数学和计算技术来计算实李群和p进李群的幺正对偶。特别是我们计划开发一套计算李群和酉表示的结构理论的软件包。该项目的影响是通过我们的第二个目标来解决的，这个目标是使关于李群和表示理论的信息对一般数学读者来说是可访问的。这将通过一个网站来完成，该网站将包含用于访问李群和表示数据的交互式工具。我们将开发的软件将是公开的，并提供广泛的文档和设计良好的用户界面。该项目还将对教育产生影响，因为它为新的研究人员提供了一种了解该领域并为之做出贡献的机制。此外，它将产生许多非专家也能处理的数学和计算问题，并将集中和组织该领域的状态，使其更易于访问。我们希望这个项目能像有限群图集对有限群理论的影响一样，对李论产生更大的影响。