We construct a model for the space of automorphisms of a connected –compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a –compact group can be lifted to a group action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper ‘The classification of 2-compact groups’ [arXiv:math.AT/0611437], where we prove the conjectured classification of –compact groups and determine their automorphism spaces.
"Automorphisms of $p$–compact groups and their root data." Geom. Topol. 12 (3) 1427 - 1460, 2008. https://doi.org/10.2140/gt.2008.12.1427