Computing SL(2,C) Central Functions with Spin Networks

Let G=SL(2,C) and F_r be a rank r free group. Given an admissible weight in N^{3r-3}, there exists a class function defined on Hom(F_r,G) called a central function. We show that these functions admit a combinatorial description in terms of graphs called trace diagrams. We then describe two algorithms (implemented in Mathematica) to compute these functions.