2009-xx Computing SL(2,C) Central Functions with Spin Networks

Computing SL(2,C) Central Functions with Spin Networks (with Sean Lawton), to appear in Geometry Dedicatae. arXiv:0903.2372 (see also this mathematica notebook with combinatorial recurrence implementation)

Abstract: Let $G=\mathrm{SL}(2,\mathbb{C})$ and $F_r$ be a rank r free group. Given an admissible weight in $N^{3r-3}$, there exists a class function defined on $\mathrm{Hom}(F_r,G)$ 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.