Cluster realizations of Weyl groups and higher Teichmüller theory

Rei Inoue, Tsukasa Ishibashi, Hironori Oya

For a symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$, we construct a family of weighted quivers $Q_m(\mathfrak{g})$ ($m\ge 2$) whose cluster modular group $Γ_{Q_m(\mathfrak{g…