We consider the problem of the decomposition of the R\'enyi entanglement
entropies in theories with a non-abelian symmetry by doing a thorough analysis
of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study
and then generalise to an arbitrary non-abelian Lie group. We find that at
leading order in the subsystem size $L$ the entanglement is equally distributed
among the different sectors labelled by the irreducible representation of the
associated algebra. We also identify the leading term that breaks this
equipartition: it does not depend on $L$ but only on the dimension of the
representation. Moreover, a $\log\log L$ contribution to the R\'enyi entropies
exhibits a universal form related to the underlying symmetry group of the
model, i.e. the dimension of the Lie group.
