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arXiv · 2001.10596

A new symmetry of the colored Alexander polynomial

V. Mishnyakov·A. Sleptsov·N. Tselousov
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Abstract

We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum $\mathfrak{sl}_N$ invariant widely known as the colored HOMFLY-PT polynomial. We provide arguments in support of the existence of the symmetry by studying the loop expansion and the character expansion of the colored HOMFLY-PT polynomial. We study the constraints this symmetry imposes on the group theoretic structure of the loop expansion and provide solutions to those constraints. The symmetry is a powerful tool for research on polynomial knot invariants and in the end we suggest several possible applications of the symmetry.

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BibTeXRIS

V. Mishnyakov, A. Sleptsov, N. Tselousov. 2020-01-28. A new symmetry of the colored Alexander polynomial. https://doi.org/10.1007/s00023-020-00980-8

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