We give a more building-oriented and somewhat simpler proof of the « saturation » theorem of Kapovich and Millson for any complex semisimple group. The main difference with their approach lies in the combinatorial part of the proof. We state a theorem of folding/unfolding triangles in the affine building, only in combinatorial terms. For the analytical part, we gather materials that appear in distinct papers of Kapovich, Leeb and Millson to complete the proof.
Cite this article
Nicole Bardy-Panse, Cyril Charignon, Stéphane Gaussent, Guy Rousseau, Une preuve plus immobilière du théorème de «saturation» de Kapovich–Leeb–Millson. Enseign. Math. 59 (2013), no. 1, pp. 3–37