  Ocneanu rigidity implies that there are finitely many (braided) fusion
categories with a given set of fusion rules. While there is no method for
determining all such categories up to equivalence, there are a few cases for
which can. For example, Kazhdan and Wenzl described all fusion categories with
fusion rules isomorphic to those of $SU(N)_k$. In this paper we extend their
results to a statement about braided fusion categories, and obtain similar
results for certain subcategories of $SU(N)_k$.
