Daniel C. Douglas
Published 2021-03-07Version 1
We show that the Fock-Goncharov quantum 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 and Goncharov called snakes. This relationship between higher Teichm\"uller theory and quantum group theory is integral to the construction of a $\mathrm{SL}_n(\mathbb{C})$-quantum trace map for links in thickened surfaces, developed in a companion paper (arXiv:2101.06817).
Comments: 29 pages, 21 figures. arXiv admin note: text overlap with arXiv:2101.06817
Quantum traces for $\mathrm{SL}_n(\mathbb{C})$: the case $n=3$
Quantum Teichmüller spaces and quantum trace map
Over then Under Tangles
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