Mathematical Sciences: Lie Groups

这个项目是数学研究中的表征 李群理论 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。 更具体地说，沃尔夫教授将完成一项关于 Harish-Chandra理论在一般真实的上的推广 半单李群 他将完成 最近发展的二元性的某些重要后果 两个哈里什-钱德拉模的构造之间的联系。 他将 完成并应用一个项目的结果， 所有常见的解析和几何 可容许表示的构造等价于 约化李群 他研究计划的另一个方面 关于表征理论和复杂性之间的相互作用 分析.

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, Professor Wolf will complete work on an extension of the theory of Harish - Chandra to general real semisimple Lie groups. He will complete the development of certain important consequences of the recently developed duality between two constructions of Harish - Chandra modules. He will complete and apply the results of a project that shows in a rather explicit way how all the usual analytic and geometric constructions of admissible representations are equivalent for reductive Lie groups. A further aspect of his research plan concerns the interplay between representation theory and complex analysis.