Indexed on: 25 Mar '16Published on: 25 Mar '16Published in: Mathematics - Operator Algebras
We associate a rigid C*-tensor category $C$ to a totally disconnected locally compact group $G$ and a compact open subgroup $K < G$. We characterize when $C$ has the Haagerup property or property (T), and when $C$ is weakly amenable. When $G$ is compactly generated, we prove that $C$ is essentially equivalent to the planar algebra associated by Jones and Burstein to a group acting on a locally finite bipartite graph. We then concretely realize $C$ as the category of bimodules generated by a hyperfinite subfactor.