Comptes Rendus
Combinatoire, Théorie des représentations
Compactly supported cohomology of a tower of graphs and generic representations of PGL n over a local field
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1133-1149.

Let F be a non-archimedean locally compact field and let G n be the group PGL n (F). In this paper we construct a tower (X ˜ k ) k0 of graphs fibred over the one-skeleton of the Bruhat–Tits building of G n . We prove that a non-spherical and irreducible generic complex representation of G n can be realized as a quotient of the compactly supported cohomology of the graph X ˜ k for k large enough. Moreover, when the representation is cuspidal then it has a unique realization in a such model.

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DOI : 10.5802/crmath.485
Classification : 22E50, 20E42

Anis Rajhi 1, 2

1 Department of quantitative methods, Higher business school of Tunis, Manouba University, Manouba 2010, Tunisia
2 Department of mathematics, Faculty of Sciences and Humanities in Dawadmi, Shaqra University, 11911 Shaqra, Saudi Arabia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Compactly supported cohomology of a tower of graphs and generic representations of $\protect \mathrm{PGL}_{n}$ over a local field},
     journal = {Comptes Rendus. Math\'ematique},
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     doi = {10.5802/crmath.485},
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Anis Rajhi. Compactly supported cohomology of a tower of graphs and generic representations of $\protect \mathrm{PGL}_{n}$ over a local field. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1133-1149. doi : 10.5802/crmath.485. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.485/

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