This project is concerned with research on algebraic groups. The principal investigator will study the action of a reductive complex algebraic group on complex n-space in an effort to classify those actions which cannot be linearized. He will also investigate the conjecture that the algebra of differential operators on quotient spaces of a complex affine variety is finitely generated. 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.
