The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms
Quantum Algebra
2026-04-30 v2
Abstract
We derive an explicit formula for the holonomy -matrix of quantum 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.
Cite
@article{arxiv.2509.02354,
title = {The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms},
author = {Calvin McPhail-Snyder and Nicolai Reshetikhin},
journal= {arXiv preprint arXiv:2509.02354},
year = {2026}
}
Comments
37 + 4 pages. Revised version, some material moved to arXiv:2509.02365