Geodesic
Combinatoire, Théorie des représentations
Compactly supported cohomology of a tower of graphs and generic representations of PGL n over a local field
Rajhi, Anis1, 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
Comptes Rendus. Mathématique, Tome 361 (2023) no. G7, pp. 1133-1149

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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 ) k⩾0 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

Rajhi, Anis 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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     author = {Rajhi, Anis},
     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},
     pages = {1133--1149},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     number = {G7},
     year = {2023},
     doi = {10.5802/crmath.485},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/crmath.485/}
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Rajhi, Anis. Compactly supported cohomology of a tower of graphs and generic representations of $\protect \mathrm{PGL}_{n}$ over a local field. Comptes Rendus. Mathématique, Tome 361 (2023) no. G7, pp. 1133-1149. doi: 10.5802/crmath.485

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