Points of quantum $\mathrm{SL}_n$ coming from quantum snakes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916606809997312 |
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| author | Douglas, Daniel C. |
| author_facet | Douglas, Daniel C. |
| contents | We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group $\mathrm{SL}_n^q$. The proof employs a quantum version of the technology invented by Fock-Goncharov called snakes. This relationship between higher Teichmüller theory and quantum group theory is integral to the construction of a $\mathrm{SL}_n$-quantum trace map for knots in thickened surfaces, partially developed in a companion paper (arXiv:2101.06817). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_04471 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Points of quantum $\mathrm{SL}_n$ coming from quantum snakes Douglas, Daniel C. Geometric Topology Quantum Algebra 2020: 57K31, 32G15, 20G42 We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group $\mathrm{SL}_n^q$. The proof employs a quantum version of the technology invented by Fock-Goncharov called snakes. This relationship between higher Teichmüller theory and quantum group theory is integral to the construction of a $\mathrm{SL}_n$-quantum trace map for knots in thickened surfaces, partially developed in a companion paper (arXiv:2101.06817). |
| title | Points of quantum $\mathrm{SL}_n$ coming from quantum snakes |
| topic | Geometric Topology Quantum Algebra 2020: 57K31, 32G15, 20G42 |
| url | https://arxiv.org/abs/2103.04471 |