Rhizospheres in spherical buildings (Q2405960)

This is a contribution to the theory of descent in buildings developed in [the first author et al., Descent in buildings. Princeton, NJ: Princeton University Press (2015; Zbl 1338.51002)]. Let \(\Gamma\) be an automorphism group of a spherical Moufang building acting with finite orbits on the set of chambers. The authors give sufficient conditions for \(\Gamma\) to be a descent group, or to be completely reducible in the sense of \textit{J.-P. Serre} [in: Séminaire Bourbaki. Volume 2003/2004. Exposés 924--937. Paris: Société Mathématique de France. 195--217, Exp. No. 932 (2005; Zbl 1156.20313)].