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Pointwise stabilizer of an apartment of the Bruhat-Tits building of $\mathrm{SL}_n(\mathbb{Q}_p)$
Denote by $X$ the Bruhat-Tits building of $\mathrm{SL}_n(\mathbb{Q}_p)$. Let $\Sigma$ be the fundamental apartment of $X$. Let $\Gamma=\mathrm{SL}_n(\mathbb{Z}[\frac{1}{p}])$.
We can prove that the ...