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.