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• W3101405613 endingPage "1611" @default.
• W3101405613 startingPage "1577" @default.
• W3101405613 abstract "For a simple linear algebraic group $G$ acting faithfully on a vector space $V$ and under mild assumptions, we show: if $V$ is large enough, then the Lie algebra of $G$ acts generically freely on $V$. That is, the stabilizer in the Lie algebra of $G$ of a generic vector in $V$ is zero. The bound on $dim V$ grows like $(mathrm{rank} G)^2$ and holds with only mild hypotheses on the characteristic of the underlying field. The proof relies on results on generation of Lie algebras by conjugates of an element that may be of independent interest. We use the bound in subsequent works to determine which irreducible faithful representations are generically free, with no hypothesis on the characteristic of the field. This in turn has applications to the question of which representations have a stabilizer in general position as well as the determination of the invariants of the representation." @default.
• W3101405613 created "2020-11-23" @default.
• W3101405613 creator A5070726537 @default.
• W3101405613 creator A5074257800 @default.
• W3101405613 date "2020-07-30" @default.
• W3101405613 modified "2023-10-14" @default.
• W3101405613 title "Generically free representations, I: large representations" @default.
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• W3101405613 doi "https://doi.org/10.2140/ant.2020.14.1577" @default.
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