Abstract
Let \({G={\rm SL}(2,\mathbb{C})}\) and \({{\tt F}_r}\) be a rank r free group. Given an admissible weight \({\vec{\lambda}}\) in \({\mathbb{N}^{3r-3}}\), there exists a class function defined on \({{\rm Hom}({\tt F}_r,G)}\) 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.
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Lawton, S., Peterson, E. Computing \({{\rm SL}(2,\mathbb{C})}\) central functions with spin networks. Geom Dedicata 153, 73–105 (2011). https://doi.org/10.1007/s10711-010-9557-9
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DOI: https://doi.org/10.1007/s10711-010-9557-9