Mathematical Sciences: Cells of Harish-Chandra Modules and the Jacquet Functor

DMS-9504778 PI：麦戈文·麦戈文将研究实经典群的Harish-Chandra模的双胞格，试图同时将它们理解为复Weyl群的集合和模。使用的主要工具是Garfinkle的标准多米诺场景。其主要目的是证明每一个实细胞都是一个复细胞的模同构。这意味着任何分次Jacquet函子都可以被实现为易于计算的跨墙算子的组合/以挪威数学家索菲斯·李的名字命名的李群理论一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

DMS-9504778 PI: McGovern McGovern will study double cells of Harish-Chandra modules for real classical groups, seeking to understand them simultaneously as sets and modules for the complex Weyl group. The main tool to be used is Garfinkle's standard domino tableaux. The main objective is show that every real cell is isomorphic as a based module to a complex cell. This implies that any graded Jacquet functor can be realized as a composition of wall-crossing operators which are easy to compute/ The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.