Symmetric invariants related to representations of exceptional simple   groups
  We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak g={\sf Lie}(G)$ such that the symmetric invariants of the semi-direct product $\mathfrak g\ltimes V$, where $V$ is an Abelian ideal, form a polynomial ring. 
Dmitri I. Panyushev and Oksana S. Yakimova
math.RT