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Buan, Iyama, Reiten and Smith proved that the superpotential of a quivercorresponding to an element of Coxeter group is rigid. In this paper, we extendthis result to the Berenstein-Fomin-Zelevinsky quivers corresponding to doubleBruhat cells of symmetric Kac-Moody algebras. We also realize these quivers asdimers models on cylinder over corresponding graphs.

Rigid potentials for cluster algebras from double Bruhat cells