Receding polar regions of a spherical building and the center conjecture

Mühlherr, Bernhard; Weiss, Richard M.

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.

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

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