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Computing SL(2, C) central functions with spin networks

Sean Lawton
Organization: Instituto Superior Tecnico
Department: Math
Elisha Peterson
Journal / Anthology

Geometriae Dedicata
Year: 2011
Volume: 153
Issue: 1
Page range: 73-105

Let G = SL(2,C) and Fr be a rank r free group. Given an admissible weight λ in N3r−3, there exists a class function defined on Hom(Fr , 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.