Complex integral geometry

复杂积分几何

• 批准号: 0070816
• 负责人: Simon Gindikin
• 金额: $ 9.6万
• 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: 2000
• 资助国家: 美国
• 起止时间: 2000-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070816&HistoricalAwards=false
• 关键词: Complex; integral; geometry

AbstractGindikinThe focus of the proposal is the development of a method of complexhorospheras for real affine symmetric spaces, including real semisimpleLie groups. We anticipate to apply this method to the construction of themodels of series of representations and to the decomposition of the regularrepresentations on series on the language of Hardy spaces ofcohomology. As one of application we hope to give an integral geometrical proof of the product-formula for c-function of Harishi-Chandra. Another direction of my research is the investigation of geometrical and analytic properties ofthe crowns of Riemann symmetric spaces - their canonical Steinneighborhoods. Integral geometry is a branch of geometrical analysis whichinvestigates integral transforms associated with different geometricalstructures. The principal challenge is to find a geometrical setting, moregeneral than the group one, where it is possible to develop a non-abelianharmonic analysis. Another direction considers complex constructionsresponsible for the geometry of real affine symmetric spaces. Suchphenomena have roots in classical geometry of Poncelet and Pluecker.

摘要Gindikin 该提案的重点是开发一种用于实仿射对称空间（包括实半单李群）的复星域方法。我们期望将该方法应用于表示系列模型的构造以及上同调 Hardy 空间语言上系列的正则表示的分解。作为应用之一，我们希望给出 Harishi-Chandra 的 c 函数的乘积公式的积分几何证明。我研究的另一个方向是研究黎曼对称空间的冠部（它们的规范斯坦邻域）的几何和解析性质。积分几何是几何分析的一个分支，研究与不同几何结构相关的积分变换。主要的挑战是找到一种比第一组更通用的几何设置，可以开发非阿贝尔调和分析。另一个方向考虑复杂的构造负责实仿射对称空间的几何形状。这种现象根源于庞塞莱和普鲁克的经典几何学。