Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.
Braiding for the quantum gl_2 at roots of unity
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abstract
In our preceding papers we started considering the categories of tangles with flat G-connections in their complements, where G is a simple complex algebraic group. The braiding (or the commutativity constraint) in such categories satisfies the holonomy Yang-Baxter equation and it is this property which is essential for our construction of invariants of tangles with flat G-connections in their complements. In this paper, to any pair of irreducible modules over the quantized universal enveloping algebra of gl_2 at a root of unity, we associate a solution of the holonomy Yang-Baxter equation.
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The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms
Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.