Mathematical Sciences: Representation Theory of Reductive P-Adic Groups

DMS-9500973 PI：MOY MOY将从不同方面研究p-进还原群的表示理论。这将包括研究特征标的行为，其中表示的局部特征标扩展被证明与出现在表示中的紧开子群的某些表示相关联，以及基于未精化的极小K型的结果发展约化p-进群的极小K型理论。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

DMS-9500973 PI: Moy Moy will investigate various aspects of the representation theory of p-adic reductive groups. This will include investigations into the behavior of characters in which the local character expansion of a representation is shown to be connected to certain representations of compact open subgroups appearing in the representation, and the development of the theory of minimal K-types for reductive p-adic groups based on the results of unrefined minimal K-types. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.