Generic stabilizers in actions of simple algebraic groups
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Journal Title
Memoirs of the American Mathematical Society
ISSN
0065-9266
Publisher
American Mathematical Society
Type
Article
This Version
AM
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Lawther, R., & Guralnick, R. M. Generic stabilizers in actions of simple algebraic groups. Memoirs of the American Mathematical Society https://doi.org/10.17863/CAM.81756
Abstract
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception, there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.
Embargo Lift Date
2025-02-22
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.81756
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334343
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
Licence URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
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