On vector invariants of the symmetric group

Abstract

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[x11 , ... ,x1,,; ••• ;x,,,1, ••• ,x.u,l with respect to the symmetric group G = S,,. 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.