On the volume conjecture for classical spin networks

Abstract

We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the spectral radius, for the special class of generalized drum graphs. Our proof uses a version of Feynman diagram calculus which we developed as a tool for the interpretation of the symbolic method of classical invariant theory, in a manner which is rigorous yet true to the spirit of the classical literature.