Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918012727066624 |
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| author | Morozov, Andrey Popolitov, Aleksandr Sleptsov, Alexei |
| author_facet | Morozov, Andrey Popolitov, Aleksandr Sleptsov, Alexei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism Morozov, Andrey Popolitov, Aleksandr Sleptsov, Alexei Mathematical Physics High Energy Physics - Theory Geometric Topology Quantum Algebra 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. |
| title | Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism |
| topic | Mathematical Physics High Energy Physics - Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2410.13676 |