The intertwiner spaces of non-easy group-theoretical quantum groups

Abstract: In 2015, Raum and Weber gave a definition of group-theoretical quantum groups, a class of compact matrix quantum groups with a certain presentation as semi-direct product quantum groups, and studied the case of easy quantum groups. In this article we determine the intertwiner spaces of non-easy group-theoretical quantum groups. We generalise group-theoretical categories of partitions and use a fiber functor to map partitions to linear maps which is slightly different from the one for easy quantum groups. We show that this construction provides the intertwiner spaces of group-theoretical quantum groups in general.