Abstract
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 \(G:X \times X \times X \times \cdot \cdot \cdot \times X\) (m copies) is stable for any \(m \geqslant n\).
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Arzhantsev, I.V. On the Stability of Diagonal Actions. Mathematical Notes 71, 735–738 (2002). https://doi.org/10.1023/A:1015808526128
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DOI: https://doi.org/10.1023/A:1015808526128