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.
