Mathematical Sciences: Representation Theory and Differential Geometry

数学科学：表示论和微分几何

• 批准号: 9009450
• 负责人: Bertram Kostant
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009450&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Differential

The principal investigator will study the implications in mathematical physics of the minimal representation of SO(4,4), completely integrable systems using "pairs of Hamiltonian operators," G-invariant differential operators on the nil-cone, and Lusztig's basis theorem. The project to be undertaken by the principal investigator involves techniques from group theory and will have consequences in mathematical physics. A group is an abstract algebraic concept which simply involves a collection of numbers or variables and a prescribed manner of combining them which obeys certain rules. The integers with the operation of addition is an example of a group. By the 1970s mathematical physicists understood that relationships between subatomic particles could be described using the group theory which had been studied for many years by algebraists.

主要研究人员将研究SO(4，4)的最小表示、使用“哈密尔顿算子对”的完全可积系统、零锥上的G-不变微分算子以及Lusztig基本定理在数学物理中的含义。由首席研究人员负责的项目涉及群论中的技术，并将在数学物理中产生影响。群是一个抽象的代数概念，它只是涉及数字或变量的集合，以及遵循一定规则的将它们组合在一起的规定方式。带加法运算的整数是群的一个例子。到20世纪70年代，数学物理学家认识到，亚原子粒子之间的关系可以用代数学家研究多年的群论来描述。