  We study the fusion semirings arising from easy quantum groups. We classify
all the possible free ones, answering a question of T. Banica and R. Vergnioux
: these are exactly the fusion rings of quantum groups without any nontrivial
one-dimensional representation. We then classify the possible groups of
one-dimensional representations for free easy quantum groups. As an
application, we give a unified proof of the Haagerup property for a broad class
of easy quantum groups, recovering as special cases previous results by M.
Brannan and F. Lemeux. We end with some considerations on the description of
the full fusion ring in the general case.
