3 papers
math.QA2024
BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity
Matthew Rupert
We consider the category of generalized weight modules over the unrolled restricted quantum group of a finite-dimensional simple complex Lie algebr…
math.RT2024
Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
Matthew Rupert
Motivated by connections to the singlet vertex operator algebra in the case, we study the unrolled restricted quantum groups $\overline{U}_q^H(\mathf…
math.CT2024
Preservation of Loewy Diagrams Under Exact Functors
Matthew Rupert
We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditio…