Asymptotics of LQG fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.