A cluster realization of $U_q(\mathfrak{s}{\mathfrak{l}}_{\mathfrak{n}})$ from quantum character varieties

Gus Schrader, Alexander Shapiro

We construct an injective algebra homomorphism of the quantum group $U_q({\mathfrak{sl}}_{n+1})$ into a quantum cluster algebra ${\mathbf{L}}_n$ associated to the moduli space of frame…