Theory of invariants and applications

不变量理论及其应用

• 批准号: 5285-2007
• 负责人: Djokovic, DragomirZ
• 金额: $ 1.17万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=449795
• 关键词: Theory; invariants; applications

We shall analyze the structure of the algebra of polynomial invariants of a classical group G such as GL_n, SO_n, O_n and Sp_{2n} acting on pairs of matrices (X,Y) of appropriate size (n or 2n) by simultaneous conjugation. In particular our intention is to compute (for some small values of n) the Poincare series, a minimal set of homogeneous generators, a homogeneous system of parameters, the corresponding Hironaka decomposition and also to describe the Hilbert's null-cone for the action. Such explicit results are known only in a handful of cases and it is important to have these data available for various applications. For instance these results may be used in the study of algebras satisfying polynomial identities.

我们将通过同时共轭分析作用于适当大小（n 或 2n）的矩阵对（X，Y）的经典群 G（例如 GL_n、SO_n、O_n 和 Sp_{2n}）的多项式不变量的代数结构。特别是，我们的目的是计算（对于 n 的某些小值）庞加莱级数、齐次生成器的最小集合、齐次参数系统、相应的 Hironaka 分解以及描述作用的希尔伯特零锥。此类明确的结果仅在少数情况下已知，因此将这些数据可用于各种应用非常重要。例如，这些结果可以用于满足多项式恒等式的代数的研究。