Mathematical Sciences: Representation Theory of P-adic Groups

这个项目是关于可接受的 p-adic域上约化群的表示理论 尤其是， 这些群的不可约表示的集合。的 主要研究人员将致力于对 通过限制到某个紧的、开的可容许对偶 子群;与抛物归纳法的关系;以及 与朗兰兹函数性和豪理论的兼容性 theta对应 本研究福尔斯属于广义p-adic范畴 代数群从历史上看，代数群出现在一个 描述一个物体的所有变换或对称性的努力 n维空间这里考虑的空间， 然而，我们熟悉的真实的空间， 平面，但完全断开的对象，是重要的， 数论和纯代数。

This project is concerned with the admissible representation theory of reductive groups over p-adic fields and, in particular, the various correspondences between the sets of irreducible representations of these groups. The principal investigators will work on the classification of the admissible dual via restriction to certain compact, open subgroups; relations with parabolic induction; and compatibility with Langlands functoriality and Howe's theory of the theta correspondence. 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 totally disconnected objects that are important in number theory and pure algebra.