Let $G$ be a group and let $V$ be a finitedimensional $G$-module. Let $B$ denote the algebra of $G$-invariantpolynomial differential operators on $V$. It is natural to pose thefollowing questions:1) What is the representation theory of $B$? What are the primitiveideals of $B$?2) Does $B$ have finite dimensional representations? If so, are theycompletely reducible?medskip oindentLittle is known about these questions when $G$ is noncommutative. Wegive answers for the adjoint representation of SL$_3(C)$, alreadyan interesting and difficult case.