Geometric Methods in Representation Theory

表示论中的几何方法

• 批准号: 1802328
• 负责人: Shrawan Kumar
• 金额: $ 15万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1802328&HistoricalAwards=false
• 关键词: Geometric; Methods; Representation; Theory

This is a project in Lie theory and geometry. Named after the mathematician Sophus Lie, Lie theory may be described as the study of symmetries of spaces of solutions of systems of differential equations. Especially important are systems of equations that model classical and quantum mechanics. Geometric properties of solution spaces encode properties of the physical systems being modeled by the differential equations. This project will develop the connections between the geometric properties and symmetries of these solution spaces, using mainly algebraic techniques. The research will focus on four specific projects. The first project will find a twisted analog of conformal blocks and the Verlinde formula, the second project is to determine an irredundant set of Inequalities for the saturated tensor cone of a Kac-Moody Lie algebra, the third project will generalize the classical Jacobson-Morozov Theorem to symmetrizable Kac-Moody Lie Algebras, and the fourth project is to develop a general topological analog of Fulton's Conjecture for group restrictions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这是李理论和几何中的一个项目。李理论以数学家 Sophus Lie 的名字命名，可以描述为对微分方程组解空间对称性的研究。尤其重要的是模拟经典力学和量子力学的方程组。解空间的几何特性编码了由微分方程建模的物理系统的特性。该项目将主要使用代数技术来开发这些解空间的几何性质和对称性之间的联系。该研究将集中在四个具体项目上。第一个项目将找到共角块和 Verlinde 公式的扭曲模拟，第二个项目是确定 Kac-Moody 李代数的饱和张量锥的一组不等式，第三个项目将推广经典 Jacobson-Morozov可对称 Kac-Moody 李代数定理，第四个项目是为群开发富尔顿猜想的一般拓扑模拟该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Elliptic classes of Schubert varieties

舒伯特簇的椭圆类

• DOI: 10.1007/s00208-020-02043-z
• 发表时间: 2020-10
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Kumar, Shrawan;Rimányi, Richárd;Weber, Andrzej
• 通讯作者: Weber, Andrzej

A COMPLETE SET OF INTERTWINERS FOR ARBITRARY TENSOR PRODUCT REPRESENTATIONS VIA CURRENT ALGEBRAS

通过当前代数表示任意张量积的完整交织器

• DOI: 10.1007/s00031-017-9454-5
• 发表时间: 2019-03
• 期刊: Transformation Groups
• 影响因子: 0.7
• 作者: KUMAR; SHRAWAN
• 通讯作者: SHRAWAN