Mathematical Sciences: Research in Representation Theory andAutomorphic Forms

数学科学：表示论和自守形式研究

• 批准号: 9003206
• 负责人: Nolan Wallach
• 金额: $ 4.09万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003206&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Representation; Theory

Professor Wallach will continue his research in the general area of group representation theory. In particular his research will involve a generalization of the Kuznetsov formula and the Laplacian on locally symmetric spaces. In addition he will study the asymptotic behavior of Whittaker functionals in the theory of the Toda lattice and further projects in the area of direct integral decompositions of reducible real reductive groups. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group. Professor Wallach's investigations involve representations of groups which have geometrical or physical content.

Wallach教授将继续他在群代表理论一般领域的研究。特别是，他的研究将涉及到局部对称空间上库兹涅佐夫公式和拉普拉斯公式的推广。此外，他还将研究Toda格理论中Whittaker泛函的渐近行为，以及可约实约群的直接积分分解领域的进一步项目。群论基本上是对称论。举一个简单的例子，当所讨论的系统在空间原点的位置改变时是不变的，自然就产生了翻译群。虽然群是抽象的对象，但特殊情况需要对称群的具体实现或“表示”。Wallach教授的研究涉及具有几何或物理内容的群的表示。