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$ G$-complete reducibility in non-connected groups


Authors: Michael Bate, Sebastian Herpel, Benjamin Martin and Gerhard Röhrle
Journal: Proc. Amer. Math. Soc. 143 (2015), 1085-1100
MSC (2010): Primary 20G15
DOI: https://doi.org/10.1090/S0002-9939-2014-12348-3
Published electronically: November 12, 2014
MathSciNet review: 3293724
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Abstract: In this paper we present an algorithm for determining whether a subgroup $ H$ of a non-connected reductive group $ G$ is $ G$-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of $ G^0$ is $ G^0$-cr. This essentially reduces the problem of determining $ G$-complete reducibility to the connected case.


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Additional Information

Michael Bate
Affiliation: Department of Mathematics, University of York, York YO10 5DD, United Kingdom
Email: michael.bate@york.ac.uk

Sebastian Herpel
Affiliation: Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
Address at time of publication: Ruhr-Universität Bochum, Fakultät für Mathematik, D-44780 Bochum, Germany
Email: herpel@mathematik.uni-kl.de, sebastian.herpel@rub.de

Benjamin Martin
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Email: Ben.Martin@auckland.ac.nz

Gerhard Röhrle
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
Email: gerhard.roehrle@rub.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12348-3
Keywords: $G$-complete reducibility, non-connected reductive groups
Received by editor(s): March 8, 2013
Received by editor(s) in revised form: July 24, 2013
Published electronically: November 12, 2014
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.