I will describe a class of highly entangled subspaces of bipartite quantum systems arising from the representation theory of a class of compact quantum groups, called the free orthogonal quantum groups. This construction yields new examples of quantum channels with some interesting properties. In particular, it is possible to obtain large lower bounds on the minimal output entropies of these channels, while at the same time we can precisely describe the behavior of tensor products of these channels with respect to certain entangled inputs. Our analysis of tensor products turns out to relate very nicely to the Temperley-Lieb recoupling theory and the quantum 6j-symbols associated to these quantum groups. (This is joint work with Benoit Collins).