Mathematical Sciences: Nonvanishing L2-Cohomology of Arithmetic Varieties

数学科学：算术簇的不零 L2 上同调

• 批准号: 8902237
• 负责人: John Wang
• 金额: $ 5.4万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902237&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonvanishing; L2; Cohomology

This award supports the research in the representations of Lie groups by Professor John S.P. Wang of Purdue University. Dr. Wang's project is to work on a conjecture relating Zuckerman modules of a semisimple connected Lie group to the L2 cohomology of the quotient of the group by a well-chosen discrete subgroup. Professor Wang's earlier work has already provided evidence of the truth of this conjecture in many cases, and his results will be of importance not only in the general theory of Lie Groups but also in the more special field of automorphic functions. Group theory began in the early nineteenth century as a description of operations that might be done successively, and also undone, as a ninety-degree clockwise rotation is undone by the ninety-degree counterclockwise rotation. Lie groups were developed in the late part of that century by the path breaking Norwegian mathematician Sophus Lie, who was interested in the most fundamental questions concerning differential equations. Now, one hundred years later, group theory pervades modern mathematics, and the utility of Lie groups in many branches of mathematics, as well as in physics, has continued undiminished.

该奖项支持普渡大学的John S.P.Wang教授在李群表示方面的研究。王博士的项目是通过一个精心选择的离散子群，将半单连通李群的Zuckerman模与该群的商的L2上同调联系起来。王教授的早期工作已经在许多情况下证明了这一猜想的真实性，他的结果不仅在李群的一般理论中具有重要意义，而且在更特殊的自同构函数领域也将具有重要意义。群论起源于十九世纪初，用来描述既可以连续完成又可以撤消的运算，因为90度顺时针旋转被90度逆时针旋转所撤消。李群是由开创性的挪威数学家索菲斯·李在那个世纪后半叶发展起来的，他对关于微分方程的最基本的问题感兴趣。现在，一百年后的今天，群论渗透到现代数学中，李群在数学的许多分支中的作用，以及在物理学中的作用，仍然没有减少。