Bate, MichaelGeranios, HaralamposMartin, Benjamin2019-01-282019-01-282019-12Bate, M, Geranios, H & Martin, B 2019, 'Orbit Closures and Invariants', Mathematische Zeitschrift, vol. 293, no. 3-4, pp. 1121-1159. https://doi.org/10.1007/s00209-019-02228-60025-5874ArXiv: http://arxiv.org/abs/1604.00924v1ORCID: /0000-0002-6670-0857/work/54384837Mendeley: dfecbad1-a04a-3e4f-89e0-af8d01933bc3http://hdl.handle.net/2164/11836The first author would like to thank Sebastian Herpel for the conversations we had which led to the first iteration of some of the ideas in this paper, and also Stephen Donkin for some very helpful nudges towards the right literature. All three authors acknowledge the funding of EPSRC grant EP/L005328/1. We would like to thank the anonymous referee for their very insightful comments and for pointing out a subtle gap in the proof of Theorem 1.1.39621194engdouble cosetsetale sliceG-complete reducibilityGeometric invariant theoryquotient varietyQuotient varietyDouble cosetsG-Complete reducibilityÉtale sliceTUPLESCOMPLETE REDUCIBILITYINSTABILITYEtalesliceALGEBRAIC-GROUPSLIE-ALGEBRASREDUCTIVE SUBGROUPSDOUBLE COSET DENSITYCLOSED ORBITSCONJUGACY CLASSESQA MathematicsGeneral MathematicsEngineering and Physical Sciences Research Council (EPSRC)EP/L005328/1QAJournal article10.1007/s00209-019-02228-6http://www.scopus.com/inward/record.url?scp=85060604702&partnerID=8YFLogxKhttp://www.mendeley.com/research/orbit-closures-invariantshttps://abdn.pure.elsevier.com/en/en/researchoutput/orbit-closures-and-invariants(02bb85f2-4c0f-4c2a-8309-e82b90b356d0).htmlhttps://arxiv.org/abs/1604.009242933