Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Universal R-Matrix, Burau Representaion and the Melvin-Morton
  Expansion of the Colored Jones Polynomial   P. Melvin and H. Morton studied the expansion of the colored Jones polynomial
of a knot in powers of q-1 and color. They conjectured an upper bound on the
power of color versus the power of q-1. They also conjectured that the bounding
line in their expansion generated the inverse Alexander-Conway polynomial.
These conjectures were proved by D. Bar-Natan and S. Garoufalidis.
  We have conjectured that other `lines' in the Melvin-Morton expansion are
generated by rational functions with integer coefficients whose denominators
are powers of the Alexander-Conway polynomial. Here we prove this conjecture by
using the R-matrix formula for the colored Jones polynomial and presenting the
universal R-matrix as a `perturbed' Burau matrix.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: supr-con