Quantum tilting modules over local rings

Abstract

AbstractWe show that tilting modules for quantum groups over local Noetherian domains of quantum characteristic 0 exist and the indecomposable tilting modules are parametrized by their highest weight. For this, we introduce a model category associated with a Noetherian ‐domain and a root system . We show that if is of quantum characteristic , the model category contains all ‐modules that admit a Weyl filtration. If is in addition local, we study torsion phenomena in the model category. This leads to a construction of torsion free, or “maximal” objects in . We show that these correspond to tilting modules for the quantum group associated with and .