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

E. Buffenoir; Ph. Roche

doi:10.1088/0305-4470/37/2/005

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

Quantum Algebra 2009-11-10 v2

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

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@article{arxiv.math/0306040,
  title  = {An infinite product formula for $U_q(sl(2))$ dynamical coboundary element},
  author = {E. Buffenoir and Ph. Roche},
  journal= {arXiv preprint arXiv:math/0306040},
  year   = {2009}
}

Comments

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

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

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