Geometriae Dedicata

, Volume 153, Issue 1, pp 73–105 | Cite as

Computing \({{\rm SL}(2,\mathbb{C})}\) central functions with spin networks

  • Sean Lawton
  • Elisha Peterson
Original Paper


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.


Spin network Trace diagram Character variety Central function 

Mathematics Subject Classification (2000)

14R20 57M07 16W22 05C10 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.University of Texas, Pan AmericanEdinburgUSA
  2. 2.Johns Hopkins University Applied Physics LabLaurelUSA

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