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- W4287179612 abstract "We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more information than considering both the Lie algebra of $G$ and the group $G(k)$ of $k$-points. For $G$ simple and $V$ faithful and irreducible, we prove the existence of a stabilizer in general position, sometimes called a principal orbit type. We determine those $G$ and $V$ for which the stabilizer in general position is smooth, or $dim V/G < dim G$, or there is a $v in V$ whose stabilizer in $G$ is trivial." @default.
- W4287179612 created "2022-07-25" @default.
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- W4287179612 date "2021-05-19" @default.
- W4287179612 modified "2023-09-24" @default.
- W4287179612 title "Generic stabilizers for simple algebraic groups" @default.
- W4287179612 doi "https://doi.org/10.48550/arxiv.2105.09486" @default.
- W4287179612 hasPublicationYear "2021" @default.
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