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arXiv · 2603.03628

A relation between the HOMFLY-PT and Kauffman polynomials via characters

Andreani Petrou·Shinobu Hikami
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Abstract

The HOMFLY-PT and Kauffman polynomials are related to each other for special classes of knots constructed by full twists and Jucys-Murphy twists. The conditions for this relation are articulated in terms of characters of the Birman-Murakami-Wenzl algebra. The latter are the coefficients in the expansion of the Kauffman polynomial involving the quantum dimensions of SO(N+1). This expansion allows to prove the conjectural 1-1 correspondence between the HOMFLY-PT/Kauffman relation and the Harer-Zagier (HZ) factorisability for a large family of 3-strand knots. The conjecture remains open for knots with 4 and higher strands.

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Andreani Petrou, Shinobu Hikami. 2026-03-04. A relation between the HOMFLY-PT and Kauffman polynomials via characters. https://arxiv.org/abs/2603.03628

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