Dehn functions of higher rank arithmetic groups of type Aₙ in products of simple Lie groups

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Suppose Γ is an arithmetic group defined over a global field K, that the K-type of Γ is Aₙ with n ≥ 2, and that the ambient semisimple group that contains Γ as a lattice has at least two noncocompact factors. We use results from Bestvina-Eskin-Wortman and Cornulier-Tessera to show that Γ has a polynomially bounded Dehn function.