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arXiv · 2410.13676

Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism

Andrey Morozov·Aleksandr Popolitov·Alexei Sleptsov
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Abstract

We prove that normalized colored Alexander polynomial (the $A \rightarrow 1$ limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution $q \rightarrow q^{|R|}$. The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices.

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Andrey Morozov, Aleksandr Popolitov, Alexei Sleptsov. 2024-10-17. Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism. https://doi.org/10.1016/j.geomphys.2024.105410

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