Representation Theory of Reductive P-Adic Groups

Gopal Prasad将继续研究可约p进群的可容许表示的分类，根据它们对紧开子群的限制。他希望能够完善他和a . Moy开发的最小k型理论（“未完善的”），并为此目的找到Kirillov理论的合适扩展。在另一个方向上，他提出了a -n型单连通各向异性群的同余子群核的中心性的证明，并确定了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的特殊集合。本研究旨在通过对这些对称性的研究，揭示算术和几何中感兴趣的物体和图案的复杂和基本性质。理解一组对称性的一种方法是将其元素表示为矩阵。表征理论以一种系统的方式做到了这一点。最终目标是能够构造和分类所有可约p进群的表示，并由此解决有关潜在几何对象的重要问题。这很重要，因为许多有趣的算术和几何对象都有有趣的对称性，形成了一个约化p进群。

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.