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

该奖项将支持犹他大学的Hugo Rossi教授与意大利Trento Degli Studi大学的Allessandro Silva教授和Maria Welleda Baldoni-Silva教授之间的合作研究。研究人员打算从事与李群的表示理论有关的工作，这是一个在现代数学和理论物理学中相当重要的话题。更具体地说，罗西教授和其他人之前的工作导致了某些半简单李群的具体表示，使用全纯离散级数的推广作为奇异表示。合作者打算将这些研究扩展到涉及离散非全纯级数的更大类别的表示。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，罗西教授是李群表征理论的发现和研究的领导者。这门学科涉及数学和物理的许多分支，例如微分方程和基本粒子物理。研究人员的方法应该证明有助于增加我们对复分析和调和分析之间的联系、复流形的几何和李群的表示理论的理解。

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.