On separating a fixed point from zero by invariants |
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Authors: | Jonathan Elmer Martin Kohls |
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Affiliation: | 1. Department of Design Engineering and Mathematics, Middlesex University, London, UKj.elmer@mdx.ac.uk;3. Technische Universit?t München, Garching, Germany |
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Abstract: | Assume a fixed point v∈VG can be separated from zero by a homogeneous invariant f∈𝕜[V]G of degree prd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree pr, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power. |
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Keywords: | Geometrically reductive invariant theory linear algebraic groups prime characteristic |
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