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

点击翻译按钮获取中文摘要

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.