Geodesic
On vector invariants of the symmetric group
Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 48-62 
S. A. Stepanov. On vector invariants of the symmetric group. Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 48-62. http://geodesic.mathdoc.fr/item/DM_1996_8_2_a3/
@article{DM_1996_8_2_a3,
     author = {S. A. Stepanov},
     title = {On vector invariants of the symmetric group},
     journal = {Diskretnaya Matematika},
     pages = {48--62},
     year = {1996},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of this paper is to give a proof of the results announced by the author [7] in 1982 on the algebraic independence over a field $k$ of any non-degenerate system of $mn$ distinct basis invariants in the ring $k[x_{11}, \dots ,x_{1n}; \dots ; x_{m1}, \dots , x_{mn}]$ with respect to the symmetric group $G=S_{n}$. The result of this paper can be extended to the case of an arbitrary finite group.The work was partially supported by the Russian Foundation for Basic Research, Grant 94–01–01206–a.