Mathematical Sciences: Representation Theory of Reductive P-adic Groups

研究了约化p-adic群的可容许表示在紧开子群限制下的分类问题。这项工作的目标之一是获得一个很好的理解这些群体的超尖齿表示。首席研究员继续他的合作与莫伊理论的最小K型，这是可能发挥根本作用的表示理论的p进群。 首席研究员还继续研究与全局域上各向异性半单群相关的算术、几何和群论问题。 这一研究属于广义的p-adic代数群的范畴，福尔斯。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性。然而，这里所考虑的空间并不是像直线和平面那样熟悉的真实的空间，而是在数论和纯代数中很重要的相关对象。

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.