Geodesic
Regular elements in spaces of linear representations of reductive algebraic groups
Izvestiya. Mathematics, Tome 24 (1985) no. 2, pp. 383-390 
D. I. Panyushev. Regular elements in spaces of linear representations of reductive algebraic groups. Izvestiya. Mathematics, Tome 24 (1985) no. 2, pp. 383-390. http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a7/
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     author = {D. I. Panyushev},
     title = {Regular elements in spaces of linear representations of reductive algebraic groups},
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     volume = {24},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new proof is offered of a differential criterion of regularity for the adjoint representation of a semisimple connected group that does not use the existence of a section in the set of regular elements. Using the ideas of this proof, similar results are obtained for certain linear actions with a Cartan subspace, and, conversely, the existence of a section in the set of regular elements is proved. Bibliography: 7 titles.

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[6] Panyushev D. I., “O prostranstvakh orbit konechnykh i svyaznykh lineinykh grupp”, Izv. AN SSSR. Ser. matem., 46:1 (1982), 95–99 | MR | Zbl

[7] Slodowy P., Simple singularities and simple algebraic groups, Lecture Notes in Math., 815, Springer, Berlin, 1980 | MR | Zbl