Representation Theory of Reductive P-Adic Groups

还原P-Adic群的表示论

• 批准号: 9801262
• 负责人: Gopal Prasad
• 金额: $ 8.66万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-15 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801262&HistoricalAwards=false
• 关键词: Representation; Theory; Reductive; Adic; Groups

ABSTRACT Gopal Prasad Michigan 98 01262 Gopal Prasad will continue his work on the classification of admissible representations of reductive p-adic groups in terms of their restrictions to compact-open subgroups. He hopes to be able to refine the theory of ("unrefined")minimal K-types developed by him and A. Moy, and also find a suitable extension of the Kirillov theory for this purpose. In another direction, he proposes to find a proof of the centrality of the congruence subgroup kernel for simply connected anisotropic groups of type A-n and determine the normal subgroups of the group of rational points of these groups. A reductive p-adic group is the special collection of symmetries of an arithmetic or geometric object. This study is expected to unravel intricate and fundamental properties of the objects and patterns which are of interest in arithmetic and geometry through the study of these symmetries. One way to understand a group of symmetries is through a representation of its elements as matrices. Representation theory does this in a systematic way. Ultimately the goal is to be able to construct and classify all representations of the reductive p-adic groups, and from this settle important questions about the underlying geometric object. This is important because so many interesting arithmetic and geometric objects have interesting symmetries that form a reductive p-adic group.

Gopal Prasad，Michigan，98,01262，Gopal Prasad将继续他的工作，即关于约化p-进群的可容许表示对紧开子群的限制的分类。他希望能够改进他和莫伊发展的(“未改进的”)极小K型理论，并为此目的找到基里洛夫理论的适当扩展。在另一个方向上，他建议证明A-n型单连通各向异性群的同余子群核的中心性，并确定这些群的有理点群的正规子群。约化p-进群是算术或几何对象的对称性的特殊集合。通过对这些对称性的研究，这项研究有望揭开对算术和几何感兴趣的物体和图案的复杂而基本的性质。理解一组对称的一种方法是将其元素表示为矩阵。表征理论以系统的方式做到了这一点。最终的目标是能够构造和分类约化p-进群的所有表示，并由此解决关于潜在几何对象的重要问题。这一点很重要，因为许多有趣的算术和几何对象都具有有趣的对称性，这些对称性形成了一个约化的p-进群。