Asymptotics of loop quantum gravity 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 Engle-Pereira-Rovelli-Livine fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU(2)(L) x SU(2)(R) semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model