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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.
(Cohomology with compact support of a space over the Bruhat-Tits building of ${\protect \rm GL}_n$ over a local field. Cuspidal representations of level zero.)
Confluentes Mathematici, 10 no. 1 (2018), p. 95-124, doi: 10.5802/cml.47
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Class. Math.: 22E50
Keywords: Representations of the general linear $p$-adic groups, Bruhat-Tits buildings, Cohomology with compact support.

Résumé - Abstract

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

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