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arXiv · 2103.04471

Points of quantum $\mathrm{SL}_n$ coming from quantum snakes

Daniel C. Douglas
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Abstract

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 Teichm\"uller 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).

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Daniel C. Douglas. 2021-03-07. Points of quantum $\mathrm{SL}_n$ coming from quantum snakes. https://doi.org/10.2140/agt.2024.24.2537

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