Geodesic
Symmetric invariants related to representations of exceptional simple
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 2, pp. 195-207.

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We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak g=\mathsf{Lie\,} G$ such that the symmetric invariants of the semi-direct product $\mathfrak g\ltimes V\!$, where $V$ is an Abelian ideal, form a polynomial ring. 
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D. I. Panyushev; O. S. Yakimova. Symmetric invariants related to representations of exceptional simple. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 2, pp. 195-207. http://geodesic.mathdoc.fr/item/MMO_2017_78_2_a0/

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