no. 2
Receding polar regions of a spherical building and the center conjecture
[Régions polaires en recul d’un immeuble sphérique et la conjecture du centre]
Mühlherr, Bernhard1 ; Weiss, Richard M.2
1 University of Giessen Institute for Mathematics Arndtstrasse 2 35392 Giessen (Germany)
2 Tufts University Department of Mathematics 503 Boston Avenue Medford, MA 02155 (USA)
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 479-513.

Nous introduisons la notion de région polaire d’un immeuble sphérique et utilisons quelques observations simples sur les régions polaires pour donner des démonstrations élémentaires de diverses propriétés fondamentales des sous-groupes radiciels. Nous combinons certaines de ces observations avec des résultats de Timmesfeld, Balser et Lytchak pour donner une nouvelle preuve de la conjecture du centre pour les sous-complexes des chambres convexes des immeubles épais sphériques.

We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.

DOI : 10.5802/aif.2767
Classification : 20E42, 20F55, 51E24
Keywords: Spherical building, root group, the center conjecture
Mot clés : immeuble sphérique, sous-groupe radiciel, la conjecture du centre

Mühlherr, Bernhard 1 ; Weiss, Richard M. 2

1 University of Giessen Institute for Mathematics Arndtstrasse 2 35392 Giessen (Germany)
2 Tufts University Department of Mathematics 503 Boston Avenue Medford, MA 02155 (USA) 
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Mühlherr, Bernhard; Weiss, Richard M. Receding polar regions of a spherical building and the center conjecture. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 479-513. doi : 10.5802/aif.2767. https://aif.centre-mersenne.org/articles/10.5802/aif.2767/

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