Mathematical Sciences: Analysis on Semisimple Groups

首席研究员计划解决 数学分析的代表性理论 （半单）李群。 后者的一个合适的例子是 球面的旋转群。 像这样的团体很重要 因为它们出现在数学的许多领域（例如几何， 微分方程，代数数论，数学 物理学）作为对称群。 表征理论允许 一个是利用对称性解决问题。 表示论的基石是 不可约表示，特别是不可约 酉表示 首席研究员将在 对半单李的这些表示进行分类 组 先前的工作提供了大量的例子， 解决这个问题的技术，在所示的 一般性的程度是非常困难的，绝对是核心， 个话题吧 一些共同的主题已经出现，一些微妙的 出现了危重病例。 计划是追求共同的 主题，并集中注意以下概括所发挥的作用： 关键案例。

The principal investigator plans to work on problems in mathematical analysis concerning the representation theory of (semisimple) 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. The building blocks for representation theory are the irreducible representations, particularly the irreducible unitary representations. The principal investigator will work toward classifying these representations for semisimple Lie groups. Prior work provides a considerable store of examples and techniques for attacking this problem, which in the indicated degree of generality is very hard, and absolutely central to the subject. Some common themes have emerged and some subtle critical cases have appeared. The plan is to pursue the common themes and concentrate on the role played by generalizations of the critical cases.