Mathematical Sciences: The Schwartz Space of Real Reductive Lie Groups and the Theory of L-Groups

主要研究人员计划研究与李群表示理论有关的数学分析问题。后者的一个合适的例子是一个球体的旋转群。像这样的群很重要，因为它们作为对称群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）。表征理论允许人们利用对称性来解决问题。更具体地说，他们将研究真实的约化李群。与自同构形式理论的相互作用，例如通过代数群的非线性双重覆盖，将被探索。我们将继续研究一个关于约化李群的Schwartz空间的项目，重点是无穷中心情况。

The principal investigators plan to work on problems in mathematical analysis concerning 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, they will be working with real reductive Lie groups. Interactions with the theory of automorphic forms, for instance via the non-linear two-fold coverings of algebraic groups, will be explored. Work will continue on a project concerning the Schwartz space of reductive Lie groups, with emphasis on the infinite center case.