A relation between the HOMFLY-PT and Kauffman polynomials via characters
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914481425088512 |
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| author | Petrou, Andreani Hikami, Shinobu |
| author_facet | Petrou, Andreani Hikami, Shinobu |
| contents | 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. However, explicit counterexamples with 4-strands negate one side of the conjecture, i.e. the HOMFLY-PT/Kauffman relation only implies HZ factorisability for knots with braid index four or higher. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03628 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A relation between the HOMFLY-PT and Kauffman polynomials via characters Petrou, Andreani Hikami, Shinobu High Energy Physics - Theory Mathematical Physics 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. However, explicit counterexamples with 4-strands negate one side of the conjecture, i.e. the HOMFLY-PT/Kauffman relation only implies HZ factorisability for knots with braid index four or higher. |
| title | A relation between the HOMFLY-PT and Kauffman polynomials via characters |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.03628 |