Mathematical Sciences: Representation Theory For Semisimple Lie Groups

本课题是李群表示理论的数学研究。后者的一个合适的例子是球体的旋转群。这样的群很重要，因为它们以对称群的形式出现在数学的许多领域(例如，几何、微分方程、代数数论、数学物理)。表象理论允许人们在解决问题时利用对称性。更具体地说，三位主要研究者将在D-模和Harish-Chandra模的背景下研究表示的代数和解析局部化。总的主题是在给定组的代表的不同会计方案之间来回切换。这项工作涉及几个数学领域的技术和思想，例如代数几何和复几何。

This project is mathematical research in the representation theory of Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics ( e.g. geometry, differential equations,algebraic number theory, mathematical physics ) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. More specifically, the three principal investigators will study algebraic and analytic localizations of representations, in the context of D-modules and Harish-Chandra modules. The overall theme is to get back and forth between various accounting schemes for the representations of a given group. This work involves techniques and ideas from several areas of mathematics, for instance algebraic geometry and complex geometry.