Mathematical Sciences: Representation Theory and Differential Geometry

数学科学：表示论和微分几何

• 批准号: 8703278
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703278&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Differential

Bertram Kostant will continue his research in the theory of Lie groups. The work will proceed in three directions 1) a plan for carrying out geometric quantization of certain nilpotent orbits by use of quasi-invariant differential operators; 2) an approach to determine generalized exponents by the use of special Kazhdan-Lusztig polynomials in the affine case and new information on the equivariant K-theory of the corresponding infinite dimensional flag manifold; 3) an approach to establish the positive definiteness of the Hermitian structure on the space of physical states. The determination of representations whose wave front set is the closure of the Joseph orbit is an important and difficult problem. These representations are generalizations of the oscillator representation for the two fold covering of the symplectic group. The study of the Kazhdan-Lusztig polynomials for Lie groups associated with affine Lie algebras using geometry of the corresponding flag variety and its relationship with K- theory is a very important aspect of this research.

Bertram Kostant将继续他的理论研究， 李群。这项工作将从三个方面进行 对于某些幂零的几何量子化， 轨道的准不变微分算子; 2）一个 一种用特殊的方法确定广义指数的方法 仿射情形下的Kazhdan-Lusztig多项式和新的 相应的等变K-理论的信息 无限维旗流形; 3）一种建立 空间上厄米特结构的正定性 物理状态。 确定波阵面集为 约瑟夫轨道的关闭是一个重要而困难的问题， 问题.这些表示是 的二重覆盖的振子表示 辛群Kazhdan-Lusztig多项式的研究 对于与仿射李代数相关联的李群， 及其与K- 理论是本研究的一个重要方面。