Invariant Theory in Algebraic Groups

代数群中的不变理论

• 批准号: 9700740
• 负责人: Gerald Schwarz
• 金额: $ 17.61万
• 依托单位: Brandeis University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700740&HistoricalAwards=false
• 关键词: Invariant; Theory; Algebraic; Groups

SCHWARZ.abs This project concerns three topics:1) (joint with L. Helminck) Commuting involutions of a reductive group and properties of the associated fixed point groups, double coset spaces and invariants. 2) (joint with D. Wehlau) The invariants of four subspaces of n-dimensional space. 3) The structure of differential operators which are invariant under a group, those which are defined on the orbit spaces of the group and the interplay between them. Invariant theory: If one has an object with symmetries (for example, the Euclidean plane with translations and rotations), one is naturally lead to consider those properties of the object (the invariants) which remain the same under these symmetries. Invariant theory is concerned with the classification, description, etc. of invariants.

SCHWARZ.abs 该项目涉及三个主题：1）（与L.约化群的交换对合及相关不动点群、双陪集空间和不变量的性质。2)（与D。Wehlau）n维空间的四个子空间的不变量。3)在群下不变的微分算子的结构，定义在群的轨道空间上的微分算子以及它们之间的相互作用。 不变量理论：如果有一个具有对称性的物体（例如，具有平移和旋转的欧几里得平面），人们自然会考虑物体的那些性质（不变量），这些性质在这些对称性下保持不变。不变量理论涉及不变量的分类、描述等。