Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant

Details Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant

1996-05-02

arxiv.org/abs/q-alg/9605003v1

Mathematics

Quantum Algebra

20 pages, LaTeX with bezier.sty

Scientific paper

We study the asymptotic expansion of the colored Jones polynomial (the Melvin-Morton expansion) using a recursion formula for the deframed universal weight system for the $sl(2)$ Lie algebra. Combined with the formula for the universal weight system for the Lie superalgebra $gl(1|1)$ (which corresponds to the Alexander-Conway knot polynomial) this formula gives a very short proof of the Melvin-Morton conjecture relating the colored Jones invariant and the Alexander-Conway polynomial of knots.

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