Complète réductibilité
[Complete reducibility]
Séminaire Bourbaki : volume 2003/2004, exposés 924-937, Astérisque, no. 299 (2005), Talk no. 932, pp. 195-217.

The notion of complete reducibility of a linear representation Γ𝐆𝐋 n can be defined in terms of the action of Γ on the Tits building of 𝐆𝐋 n . An analogous definition can be given for any reductive group. We shall see how this translates in topological terms, and what applications can be obtained.

La notion de complète réductibilité d’une représentation linéaire Γ𝐆𝐋 n peut se définir en termes de l’action de Γ sur l’immeuble de Tits de 𝐆𝐋 n . Cela suggère une notion analogue pour tous les immeubles sphériques, et donc aussi pour tous les groupes réductifs. On verra comment cette notion se traduit en termes topologiques et quelles applications on peut en tirer.

Classification: 20-xx,  57M07
Keywords: reductive groups, spherical buildings, complete reducibility
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Serre, Jean-Pierre. Complète réductibilité, in Séminaire Bourbaki : volume 2003/2004, exposés 924-937, Astérisque, no. 299 (2005), Talk no. 932, pp. 195-217. http://archive.numdam.org/item/SB_2003-2004__46__195_0/

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