Mathematical Sciences: Algebraic Groups - Combinatorial, Geometric and Representation - Theoretic Aspects

数学科学：代数群 - 组合、几何和表示 - 理论方面

• 批准号: 9502942
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502942&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Groups; Combinatorial

This award supports work related to the combinatorial, geometric and representation-theoretic aspects of semi-simple algebra groups. In particular, the principal investigator will determine the singular loci of Schubert varieties; will determine the multiplicity of a singular point on a Schubert variety; will establish Postulation formulae for tangent cones at singular points on a Schubert variety; and will write the equations of the conormal bundle of a Schubert variety. She will also develop a Standard Monomial Theory for Quivers; and will devise a combinatorial construction for quantum groups. The research supported involves invariant theory and algebraic groups. In general, invariant theory involves the actions of linear algebraic groups on manifolds or linear spaces and the determination of the mathematical invariants of the space under these group actions.

该奖项支持与半简单代数群的组合、几何和表示论方面相关的工作。 特别是，首席研究员将确定舒伯特变体的奇异基因座；将确定舒伯特簇上奇点的重数；将建立舒伯特簇上奇点处的切锥公设公式；并将写出舒伯特簇的共正规束方程。 她还将开发箭袋的标准单项式理论；并将设计量子群的组合结构。 支持的研究涉及不变理论和代数群。 一般来说，不变量理论涉及线性代数群在流形或线性空间上的作用以及在这些群作用下空间的数学不变量的确定。