MelvinMorton conjecture and primitive Feynman diagrams
Abstract
We give a very short proof of the MelvinMorton conjecture relating the colored Jones polynomial and the Alexander polynomial of knots. The proof is based on the explicit evaluation of the corresponding weight systems on primitive elements of the Hopf algebra of chord diagrams which, in turn, follows from simple identities between fourvalent tensors on the Lie algebra $sl_2$ and the Lie superalgebra $gl(11)$. This shows that the miraculous connection between the Jones and Alexander invariants follows from the similarity (supersymmetry) between $sl_2$ and $gl(11)$.
 Publication:

eprint arXiv:qalg/9605028
 Pub Date:
 May 1996
 DOI:
 10.48550/arXiv.qalg/9605028
 arXiv:
 arXiv:qalg/9605028
 Bibcode:
 1996q.alg.....5028V
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 17 pages, LaTeX 2.09 with bezier.sty