Globally Irreducible Weyl Modules for Quantum Groups

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for \(E_{8}\) or its highest weight is minuscule. In this paper, we prove an analogous criteria for irreducibility of Weyl modules over the quantum group \(U_{\zeta }({\mathfrak {g}})\) where \({\mathfrak {g}}\) is a complex simple Lie algebra and \(\zeta \) ranges over roots of unity.