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Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de GL n sur un corps local. Représentations cuspidales de niveau zéro.
[Cohomology with compact support of a space over the Bruhat-Tits building of GL n over a local field. Cuspidal representations of level zero.]
Anis Rajhi1
1 Université de Sousse ; École supérieure des sciences et technologies de Hammam-Sousse, Hammam Sousse 4011, Tunisie
Confluentes Mathematici, Volume 10 (2018) no. 1, pp. 95-124.

Let G the group GL n (F), where F is a non-archimedean locally compact field, and 𝔅(G) its Bruhat-Tits building. We construct a simplicial complex 𝒲 ˜, equipped with an action of G and with a G-equivariant proper simplicial projection p:𝒲 ˜⟶𝔅(G). We prove that the cohomology with compact support in higher dimensions H c n-1 (𝒲 ˜,ℂ) contains as subquotients all irreducible cuspidal level zero representations.

Soit G le groupe GL n (F), où F est un corps localement compact non-archimédien, et 𝔅(G) son immeuble de Bruhat-Tits. Nous construisons un complexe simplicial 𝒲 ˜, doté d’une action de G et d’une projection propre simpliciale G-équivariante p:𝒲 ˜⟶𝔅(G). Nous démontrons qu’en dimension supérieure la cohomologie à support compact H c n-1 (𝒲 ˜,ℂ) contient comme sous-quotient toutes les représentations cuspidales irréductibles de niveau zéro.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/cml.47
Classification: 22E50
Keywords: Representations of the general linear $p$-adic groups, Bruhat-Tits buildings, Cohomology with compact support.

Anis Rajhi 1

1 Université de Sousse ; École supérieure des sciences et technologies de Hammam-Sousse, Hammam Sousse 4011, Tunisie
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     journal = {Confluentes Mathematici},
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Anis Rajhi. Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de ${\protect \rm GL}_{n}$ sur un corps local. Représentations cuspidales de niveau zéro.. Confluentes Mathematici, Volume 10 (2018) no. 1, pp. 95-124. doi : 10.5802/cml.47. https://cml.centre-mersenne.org/articles/10.5802/cml.47/

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