Globally Irreducible Weyl Modules for Quantum Groups

Abstract

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 $U_ζ({\mathfrak g})$ where ${\mathfrak g}$ is a complex simple Lie algebra and $ζ$ ranges over roots of unity.