Speaker: Gerhard Röhrle (Bochum)
Title: On a Relative Version of Serre's Notion of \(G\)-complete Reducibility
Abstract:
We explain a relative variant of Serre's notion of \(G\)-complete reducibility for a (connected) reductive algebraic group \(G\). We let \(K\) be a (connected) reductive subgroup of \(G\), and consider subgroups of \(G\) which normalise the identity component of \(K\). It turns out that such a subgroup is relatively \(G\)-completely reducible with respect to \(K\) if and only if its image in the automorphism group of \(K\) is completely reducible. This allows us to generalise a number of fundamental results from the absolute to the relative setting. This is a report on joint work with M. Gruchot and A. Litterick.