Complete reducibility: variations on a theme of Serre

Maike Gruchot, Alastair Litterick, Gerhard Röhrle
2021 Manuscripta mathematica  
AbstractIn this note, we unify and extend various concepts in the area of G-complete reducibility, where G is a reductive algebraic group. By results of Serre and Bate–Martin–Röhrle, the usual notion of G-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of G. We show that other variations of this notion, such as relative complete reducibility and $$\sigma $$ σ -complete reducibility, can also be viewed as special
more » ... es of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.
doi:10.1007/s00229-021-01318-2 fatcat:cpuffrdarnfo3h6qxpvnzci3zy