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

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 $F(x)M_1(x{q}^{h_2})M_2(x)=\Delta (M(x)).$ 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.

9 pages in latex. Proceedings of the conference ``Recent Advances in the Theory of Quantum Integrable Systems 2003'', LAPTH, Annecy-Le-Vieux remarks added to clarify the main proof

References in corpus (2)

• Harmonic Analysis on the quantum Lorentz group
• On the dynamical Yang-Baxter equation