Compactly supported cohomology of a tower of graphs and generic representations of $\protect PGL_{n}$ over a local field - Rajhi, Anis (Comptes Rendus. Mathématique)
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 $(\tilde{X}_{k})_{k\geqslant 0}$ 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 $\tilde{X}_{k}$ for $k$ large enough. Moreover, when the representation is cuspidal then it has a unique realization in a such model.