An infinite product formula for $U_q(sl(2))$ dynamical coboundary element
Buffenoir, Eric ; ROCHE, Philippe
HAL, hal-00324045 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-01-16
Classification:  PACS number: 02.20.Uw,  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] 
@article{hal-00324045,
     author = {Buffenoir, Eric and ROCHE, Philippe},
     title = {An infinite product formula for $U\_q(sl(2))$ dynamical coboundary element},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00324045}
}

Buffenoir, Eric; ROCHE, Philippe. An infinite product formula for $U_q(sl(2))$ dynamical coboundary element. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00324045/