𝐺-complete reducibility in non-connected groups

Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard

doi:10.1090/S0002-9939-2014-12348-3

$G$-complete reducibility in non-connected groups
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by Michael Bate, Sebastian Herpel, Benjamin Martin and Gerhard Röhrle

Proc. Amer. Math. Soc. 143 (2015), 1085-1100

DOI: https://doi.org/10.1090/S0002-9939-2014-12348-3

Published electronically: November 12, 2014

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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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