Geodesic
On the Stability of Diagonal Actions
Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 803-806

Voir la notice de l'article provenant de la source Math-Net.Ru

In the note it is proved that, for an arbitrary action of a semisimple group $G$ on an affine variety $X$, there is a positive integer $n$ such that the diagonal action $G:X\times X\times\dotsb\times X$ ($m$ copies) is stable for any $m\ge n$. 
@article{MZM_2002_71_6_a0,
     author = {I. V. Arzhantsev},
     title = {On the {Stability} of {Diagonal} {Actions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--806},
     publisher = {mathdoc},
     volume = {71},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a0/}
}
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I. V. Arzhantsev. On the Stability of Diagonal Actions. Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 803-806. http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a0/