The holonomy braiding for ${\mathcal{U}}_{\hat{I}}¾({\mathfrak{sl}}_2)$ in terms of geometric quantum dilogarithms

Calvin McPhail-Snyder, Nicolai Reshetikhin

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 sat…