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

DMS-9504778 PI: McGovern McGovern将研究真实经典群的Harish-Chandra模块的双细胞，试图同时将它们理解为复杂Weyl群的集合和模块。使用的主要工具是加芬克尔的标准多米诺骨牌。主要目的是证明每个真实的细胞都是同构的，作为一个基础模块的复杂细胞。这意味着任何有阶的Jacquet函子都可以被实现为易于计算的跨壁算子的组合。李群理论是为了纪念挪威数学家Sophus Lie而命名的，是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

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.