U.S.-Italy Research on Homogeneous C/R Manifolds

美国-意大利关于均质 C/R 流形的研究

• 批准号: 8717257
• 负责人: Hugo Rossi
• 金额: $ 0.67万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-01 至 1990-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8717257&HistoricalAwards=false
• 关键词: U.S.; Italy; Research; Homogeneous; Manifolds

This award will support collaborative research between Prof. Hugo Rossi of the University of Utah and Prof. Allessandro Silva and Prof. Maria Welleda Baldoni-Silva, both of the Universita Degli Studi Di Trento, in Italy. The investigators intend to pursue work related to the representation theory of Lie groups, a topic of considerable importance in modern day mathematics and in theoretical physics. More specifically, previous work of Prof. Rossi and others led to concrete representations of certain semi-simple Lie groups using generalizations of holomorphic discrete series as singular representations. The collaborators intend to extend these investigations to a much larger class of representations involving discrete non-holomorphic series. The Italian researchers bring to the collaboration expertise in analysis and geometry. On the U.S. side, Prof. Rossi has been a leader in the discovery and investigation of the representation theory of Lie groups. The subject is one that relates to many branches of mathematics and physics, for example differential equations and elementary particle physics. The investigators' approach should prove useful in increasing our understanding of the connection between complex and harmonic analysis, the geometry of complex manifolds, and the representation theory of Lie groups.

该奖项将支持犹他大学的 Hugo Rossi 教授与意大利特伦托大学的 Allessandro Silva 教授和 Maria Welleda Baldoni-Silva 教授之间的合作研究。 研究人员打算开展与李群表示论相关的工作，这是现代数学和理论物理学中相当重要的一个主题。 更具体地说，Rossi 教授和其他人之前的工作导致使用全纯离散级数的推广作为奇异表示来具体表示某些半简单李群。 合作者打算将这些研究扩展到涉及离散非全纯序列的更大类别的表示。 意大利研究人员为合作带来了分析和几何方面的专业知识。 在美国方面，罗西教授一直是李群表示论发现和研究的带头人。 该学科涉及数学和物理学的许多分支，例如微分方程和基本粒子物理学。 研究人员的方法应该有助于增强我们对复数分析与调和分析、复流形几何以及李群表示论之间的联系的理解。