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- W2805488521 abstract "Let $K$ be a reductive subgroup of a reductive group $G$ over an algebraically closed field $k$. Using the notion of relative complete reducibility, in previous work of Bate-Martin-Roehrle-Tange a purely algebraic characterization of the closed $K$-orbits in $G^n$ was given, where $K$ acts by simultaneous conjugation on $n$-tuples of elements from $G$. This characterization generalizes work of Richardson and is also a natural generalization of Serre's notion of $G$-complete reducibility. In this paper we revisit this idea, focusing on the particular case when the ambient group $G$ is a general linear group, giving a representation-theoretic characterization of relative complete reducibility. Along the way, we extend and generalize several results from the aforementioned work of Bate-Martin-Roehrle-Tange." @default.
- W2805488521 created "2018-06-13" @default.
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- W2805488521 date "2018-06-08" @default.
- W2805488521 modified "2023-09-26" @default.
- W2805488521 title "Relative $GL(V)$-complete reducibility" @default.
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