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arXiv · 2509.02354

The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms

Calvin McPhail-Snyder·Nicolai Reshetikhin
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Abstract

We derive an explicit formula for the holonomy $R$-matrix of quantum $\mathfrak{sl}_2$ at a root of unity. We show it factorizes into a product of four quantum dilogarithms and satisfies a holonomy Yang-Baxter equation. This factorization extends previously known results and we collect many existing results needed for our computation.

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Calvin McPhail-Snyder, Nicolai Reshetikhin. 2025-09-02. The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms. https://arxiv.org/abs/2509.02354

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