Mathematical Sciences: Flag and Schubert Schemes - Classical, Generalized and Quantum

数学科学：Flag 和 Schubert 方案 - 经典、广义和量子

• 批准号: 9103129
• 负责人: Venkatramani Lakshmibai
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103129&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Flag; Schubert; Schemes

This project is concerned with research related to Flag and Schubert schemes. The principal investigator will work on the following problems: (1) develop a standard monomial theory for Kac-Moody groups; (2) determine the multiplicity of a singular point on a Schubert variety; (3) develop a standard monomial theory for tangent cones at singular points on a Schubert variety; (4) determine the Kazhdan-Lusztig polynomials P(w,t) for w greater than or equal to t; (5) write the equations of the conormal bundle of a Schubert variety; (6) develop a theory of quantum Flag and Schubert schemes in the finite and affine cases. This project is concerned with the study of algebraic groups. It combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working on conformal field theory.

该项目涉及与 Flag 和 Schubert 方案相关的研究。 主要研究者将致力于以下问题：（1）开发Kac-Moody群的标准单项式理论； (2) 确定舒伯特簇上奇点的重数； (3) 发展舒伯特簇上奇点处的切锥体的标准单项式理论； (4) 确定 w 大于或等于 t 时的 Kazhdan-Lusztig 多项式 P(w,t)； (5) 写出舒伯特簇的共正规丛方程； (6) 发展有限和仿射情况下的量子Flag 和Schubert 格式的理论。 该项目涉及代数群的研究。 它结合了“纯”数学、代数、分析和几何这三个最古老的领域，但研究共形场论的物理学家对它非常感兴趣。