G-complete reducibility in non-connected groups

Öffnen
Datum
2013-04-10MFO Scientific Program
Research in Pairs 2012Serie
Oberwolfach Preprints;2013,09Autor
Bate, Michael
Herpel, Sebastian
Martin, Benjamin
Röhrle, Gerhard
Metadata
Zur LanganzeigeOWP-2013-09
Zusammenfassung
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.