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

References in corpus (2)

• Cohomology for quantum groups via the geometry of the nullcone
• Globally Irreducible Weyl Modules