Mathematical Sciences: Invariant Theory and Algebraic Groups

支持的研究项目涉及不变理论和代数变换群的三个方面。首先，主要研究者将证明复n维空间上具有适当条件的约化群作用是线性化的。第二，在紧凑的情况下，首席研究员最近的工作将扩展到一般情况。第三，G(2)的不变量将被检验。支持的研究是在不变量理论和代数群领域。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。

The research project supported concerns three aspects of invariant theory and algebraic transformation groups. First, the principal investigator will show that a reductive group action on complex n-dimensional space with suitable conditions is linearizable. Second, recent work of the principal investigator in the compact case will be extended to the general situation. Third, the invariants of G(2) will be examined. The research supported is in the area of 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.