AbstractWe present a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of type ADE. That is, we prove that there is a natural Hopf algebra isomorphism from the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras, we show that the quantum group admits a cluster canonical ...
AbstractIn this talk, we propose a new type of global symmetries: the fermionic higher-form symmetries. We discuss examples with fermionic higher-form symmetries as well as the gauging and breaking of such symmetries. The talk is based on the work 2303.12633 with Yi Zhang