Mathematical Sciences: Representation Theory of Reductive P-adic Groups

本文研究了约化p-ady群的可容许表示对紧开子群的限制的分类。这项工作的目的之一是对这些群的超尖球面表示有一个很好的理解。主要研究者继续他与Moy在极小K型理论上的合作，该理论很可能在p-Add群的表示理论中发挥基础作用。首席研究员还继续研究与全球场上的各向异性半单群有关的算术、几何和群论问题。这项研究属于广义的p-进代数群范畴。在历史上，代数群的出现是为了描述n维空间的所有变换或对称。然而，这里考虑的空间不是我们熟悉的像直线和平面这样的实空间，而是在数论和纯代数中非常重要的相关对象。

This research concerns the classification of admissible representations of reductive p-adic groups in terms of their restrictions to compact-open subgroups. One of the goals of this work is to gain a good understanding of supercuspidal representations of these groups. The principal investigator continues his collaboration with Moy on the theory of minimal K-types, which is likely to play a fundamental role in representation theory of p-adic groups. The principal investigator also continues to pursue arithmetic, geometric and group-theoretic questions related to anisotropic semi-simple groups over global fields. This research falls into the broad category of p-adic algebraic groups. Historically, algebraic groups arose in an effort to describe all the transformations or symmetries of an n-dimensional space. The spaces under consideration here, however, are not the familiar real spaces like the line and the plane, but related objects which ape important in number theory and pure algebra.