Attenborough, Christopher and Bate, Michael and Gruchot, Maike and Litterick, Alastair and Roehrle, Gerhard (2020) On relative complete reducibility. Quarterly Journal of Mathematics, 71 (1). pp. 321-334. DOI https://doi.org/10.1093/qmathj/haz044
Attenborough, Christopher and Bate, Michael and Gruchot, Maike and Litterick, Alastair and Roehrle, Gerhard (2020) On relative complete reducibility. Quarterly Journal of Mathematics, 71 (1). pp. 321-334. DOI https://doi.org/10.1093/qmathj/haz044
Attenborough, Christopher and Bate, Michael and Gruchot, Maike and Litterick, Alastair and Roehrle, Gerhard (2020) On relative complete reducibility. Quarterly Journal of Mathematics, 71 (1). pp. 321-334. DOI https://doi.org/10.1093/qmathj/haz044
Abstract
Let K be a reductive subgroup of a reductive group G over an algebraically closed field k. The notion of relative complete reducibility, introduced in previous work of Bate-Martin-Roehrle-Tange, gives a purely algebraic description of the closed K-orbits in Gn, where K acts by simultaneous conjugation on n-tuples of elements from G. This extends work of Richardson and is also a natural generalization of Serre's notion of G-complete reducibility. In this paper we revisit this idea, giving a characterization of relative G-complete reducibility which directly generalizes equivalent formulations of G-complete reducibility. If the ambient group G is a general linear group, this characterization yields representation-theoretic criteria. Along the way, we extend and generalize several results from the aforementioned work of Bate-Martin-Roehrle-Tange.
Item Type: | Article |
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Additional Information: | 10 pages; v2 15 pages; substantially revised and expanded version: most results are generalized from the case of a general linear group to an arbitrary connected reductive algebraic group. List of authors expanded. To appear in Quarterly Journal of Mathematics |
Uncontrolled Keywords: | reductive algebraic groups; G-complete reducibility; closed G-orbits |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 11 Sep 2019 11:48 |
Last Modified: | 07 Aug 2024 18:19 |
URI: | http://repository.essex.ac.uk/id/eprint/25324 |
Available files
Filename: 1806.03067.pdf