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Braiding for the quantum gl_2 at roots of unity

R. Kashaev·N. Reshetikhin
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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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R. Kashaev, N. Reshetikhin. 2004-10-06. Braiding for the quantum gl_2 at roots of unity. https://arxiv.org/abs/math/0410182

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