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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.15171 |
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| _version_ | 1866909746721718272 |
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| author | Gruen, Angus Suárez, Lara San Martín |
| author_facet | Gruen, Angus Suárez, Lara San Martín |
| contents | We construct the invariant $F_K^{\mathfrak{sl}_3}\in\mathbb{Z}[q,q^{-1}][[x,y]]$ for any positive braid knot $K$, whose existence was conjectured by Park, building on earlier work of Gukov--Manolescu. The main step in our work extends a result by the first author on the invariant associated to symmetric representations of $\mathfrak{sl}_3$ to all irreducible representations. We conclude with a conjectural framework for constructing $F_K^{\mathfrak{sl}_N}$ for arbitrary $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A large color $R$-matrix for $\mathfrak{sl}_3$ Gruen, Angus Suárez, Lara San Martín Geometric Topology High Energy Physics - Theory Mathematical Physics Quantum Algebra We construct the invariant $F_K^{\mathfrak{sl}_3}\in\mathbb{Z}[q,q^{-1}][[x,y]]$ for any positive braid knot $K$, whose existence was conjectured by Park, building on earlier work of Gukov--Manolescu. The main step in our work extends a result by the first author on the invariant associated to symmetric representations of $\mathfrak{sl}_3$ to all irreducible representations. We conclude with a conjectural framework for constructing $F_K^{\mathfrak{sl}_N}$ for arbitrary $N$. |
| title | A large color $R$-matrix for $\mathfrak{sl}_3$ |
| topic | Geometric Topology High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2508.15171 |