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Speaker:

Gerhard Röhrle
Affiliation:

Ruhr-Universität Bochum
Date:

Thu, 2018-11-22 16:30 - 17:30
Location:

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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