Mathematical Sciences: Automorphic Representations of Semisimple Lie Groups

数学科学：半单李群的自守表示

• 批准号: 8801248
• 负责人: Birgit Speh
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-15 至 1991-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801248&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Automorphic; Representations; Semisimple

The principal investigator plans to work on problems in mathematical analysis concerning the representation theory of (semisimple) Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics (e.g. geometry, differential equations, algebraic number theory, mathematical physics) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. More specifically, this project will study representations that come from spaces of automorphic forms (invariant analytic functions) on the quotient of the group modulo a discrete subgroup. The aim is to obtain explicit formulas for the multiplicities of known irreducible representations in these automorphic representations, based on algebraic properties of the discrete group and information about how it sits in the ambient Lie group.

首席研究员计划致力于数学分析中有关(半单)李群表示理论的问题。后者的一个合适的例子是球体的旋转群。这样的群很重要，因为它们以对称群的形式出现在数学的许多领域(例如，几何、微分方程、代数数论、数学物理)。表象理论允许人们在解决问题时利用对称性。更具体地说，这个项目将研究来自以离散子群为模的群的商上的自同形空间(不变解析函数)的表示。其目的是基于离散群的代数性质和关于它如何位于环境李群中的信息，得到已知不可约表示在这些自同构表示中的重数的显式公式。