$\mathcal{A}=\mathcal{U}$ for cluster algebras from moduli spaces of $G$-local systems

Tsukasa Ishibashi, Hironori Oya, Linhui Shen

For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a non-trivial minuscule representation and a connected marked surface $\Sigma$ with at least two marked points and n…