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On a relative version of Serre's notion of G-complete reducibility

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Gerhard Röhrle
Ruhr-Universität Bochum
Thu, 2018-11-22 16:30 - 17:30
MPIM Lecture Hall

We first review some basic results related to Serre's notion of
G-complete reducibility for a reductive algebraic group G. We then
discuss a relative variant of this concept where we let K be a reductive
subgroup of G, and consider subgroups of G which normalise the identity
component K^o of K. We show that such a subgroup is relatively
G-completely reducible with respect to K if and only if its image in the
automorphism group of K^o is completely reducible in the sense of Serre.
This allows us to generalise a number of fundamental results from the
absolute to the relative setting. This is a report on recent joint work
with M. Gruchot and A. Litterick.

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