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An infinite product formula for $U_q(sl(2))$ dynamical coboundary element

E. Buffenoir·Ph. Roche
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Abstract

We give a short summary of results and conjectures in the theory of dynamical quantum group related to the dynamical coboundary equation also known as IRF-Vertex transform. O.Babelon has shown that the dynamical twist $F(x)$ of $U_q(sl(2))$ is a dynamical coboundary $M(x)$ i.e $F(x)M_1(xq^{h_2})M_2(x)=Δ(M(x)).$ We give a new formula for this element $M(x)$ as an infinite product and give a new proof of the coboundary relation. Our proof involves the quantum Weyl group element, giving possible hint for the generalization to higher rank case.

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BibTeXRIS

E. Buffenoir, Ph. Roche. 2003-09-11. An infinite product formula for $U_q(sl(2))$ dynamical coboundary element. https://doi.org/10.1088/0305-4470/37/2/005

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