Quivers and the Invariant Theory of Levi Subgroups

We develop a theory of invariants using the formalism of quivers, generalizing earlier results attributed to Procesi. As an application, let H be the Levi component of a parabolic subgroup of a classical Lie group G with Lie algebra g. We describe a finite set of generators for P[g]H, the space of H-invariant polynomials on g, as well as the H-invariants in the universal enveloping algebra, U(g)H, thus generalizing the results of Klink and Ton-That, and Zhu.