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.

26 pages; A missing assumption in the statement of Theorem 4.20 has been added. In Remark 4.22 we explain the structure of the intertwiner spaces if this assumption is not satisfied. Several other minor corrections and updates have been made