Geodesic
Cubic forms on adjoint representations of exceptional groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 9-23

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We construct cubic forms on adjoint representation of the Chevalley group of type $\mathsf E_7$, whose partial derivatives are linear combinations of equations on the orbit of the highest weight vector. In order to describe the forms we introduce new combinatorial notions related to maximal squares in root systems of exceptional types. 
@article{ZNSL_2016_443_a1,
     author = {M. M. Atamanova and A. Yu. Luzgarev},
     title = {Cubic forms on adjoint representations of exceptional groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--23},
     publisher = {mathdoc},
     volume = {443},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a1/}
}
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M. M. Atamanova; A. Yu. Luzgarev. Cubic forms on adjoint representations of exceptional groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 9-23. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a1/