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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2007.15621 |
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| _version_ | 1866915450397392896 |
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| author | Yuasa, Wataru |
| author_facet | Yuasa, Wataru |
| contents | The stability of coefficients of colored ($\mathfrak{sl}_2$-) Jones polynomials $\{J_{K,n}^{\mathfrak{sl}_2}(q)\}_n$ was discovered by Dasbach and Lin. This stability is now called the zero-stability of $J_{K,n}^{\mathfrak{sl}_2}(q)$. Armond showed zero stability for a $B$-adequate link by using the linear skein theory based on the Kauffman bracket. In this paper, we prove the zero stability of one-row colored $\mathfrak{sl}_{3}$-Jones polynomials $\{J_{K,n}^{\mathfrak{sl}_3}(q)\}_n$ for $B$-adequate links $L$ with anti-parallel twist regions by using the linear skein theory based on Kuperberg's $\mathfrak{sl}_3$-webs. It implies the existence of many $q$-series obtained from a quantum invariant associated with $\mathfrak{sl}_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_15621 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The zero stability for the one-row colored $\mathfrak{sl}_3$ Jones polynomial Yuasa, Wataru Geometric Topology Quantum Algebra 57K10, 57K14, 57K16 The stability of coefficients of colored ($\mathfrak{sl}_2$-) Jones polynomials $\{J_{K,n}^{\mathfrak{sl}_2}(q)\}_n$ was discovered by Dasbach and Lin. This stability is now called the zero-stability of $J_{K,n}^{\mathfrak{sl}_2}(q)$. Armond showed zero stability for a $B$-adequate link by using the linear skein theory based on the Kauffman bracket. In this paper, we prove the zero stability of one-row colored $\mathfrak{sl}_{3}$-Jones polynomials $\{J_{K,n}^{\mathfrak{sl}_3}(q)\}_n$ for $B$-adequate links $L$ with anti-parallel twist regions by using the linear skein theory based on Kuperberg's $\mathfrak{sl}_3$-webs. It implies the existence of many $q$-series obtained from a quantum invariant associated with $\mathfrak{sl}_3$. |
| title | The zero stability for the one-row colored $\mathfrak{sl}_3$ Jones polynomial |
| topic | Geometric Topology Quantum Algebra 57K10, 57K14, 57K16 |
| url | https://arxiv.org/abs/2007.15621 |