dorsal/arxiv
View SchemaMelvin-Morton conjecture and primitive Feynman diagrams
| Authors | Arkady Vaintrob |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605028 |
| URL | https://arxiv.org/abs/q-alg/9605028 |
Abstract
We give a very short proof of the Melvin-Morton 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 four-valent tensors on the Lie algebra $sl_2$ and the Lie superalgebra $gl(1|1)$. This shows that the miraculous connection between the Jones and Alexander invariants follows from the similarity (supersymmetry) between $sl_2$ and $gl(1|1)$.
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"abstract": "We give a very short proof of the Melvin-Morton conjecture relating the\ncolored Jones polynomial and the Alexander polynomial of knots. The proof is\nbased on the explicit evaluation of the corresponding weight systems on\nprimitive elements of the Hopf algebra of chord diagrams which, in turn,\nfollows from simple identities between four-valent tensors on the Lie algebra\n$sl_2$ and the Lie superalgebra $gl(1|1)$. This shows that the miraculous\nconnection between the Jones and Alexander invariants follows from the\nsimilarity (supersymmetry) between $sl_2$ and $gl(1|1)$.",
"arxiv_id": "q-alg/9605028",
"authors": [
"Arkady Vaintrob"
],
"categories": [
"q-alg",
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"title": "Melvin-Morton conjecture and primitive Feynman diagrams",
"url": "https://arxiv.org/abs/q-alg/9605028"
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