Mathematical Sciences: Cohomological and Arithmetic Interpretation of Spectra on Certain Symmetric Spaces

数学科学：某些对称空间上谱的上同调和算术解释

• 批准号: 8802597
• 负责人: Floyd Williams
• 金额: $ 4.56万
• 依托单位: University of Massachusetts Amherst
• 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: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802597&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomological; Arithmetic; Interpretation

This project is mathematical research in 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, the situation is that of a Lie group acting on its quotient modulo a lattice, and thus on the space of square-integrable functions on the quotient. The aim is to obtain the multiplicities in this representation of certain irreducible unitary representations of the group, particularly limits of discrete series representations.

这个项目是数学研究中的表征 （半单）李群理论。 本发明的一个合适的示例是： 后者是球体的旋转群。 像这样的团体 因为它们出现在数学的许多领域 (e.g.几何，微分方程，代数数论， 数学物理学）作为对称群。 表示 理论允许人们利用对称性来解决 问题 更具体地说，情况是李群 作用于其商模格，从而作用于 商上的平方可积函数。 目的是 在这个表示中获得某些 群的不可约酉表示，特别是 离散级数表示的极限。