Integral presentations for the universal \(R\)-matrix (Q5926739)

The authors present an integral formula for the universal \(R\)-matrix of the quantum affine algebra \(U_q(\widehat{{\mathfrak g}})\) with `Drinfeld comultiplication'. They show that the properties of the universal \(R\)-matrix follow from the factorization properties of the cycles in proper configuration spaces. For general \({\mathfrak g}\) they conjecture that such cycles exist and are unique. For \(U_q(\widehat{{\mathfrak g}})\) the authors describe precisely the cycles and present a new simple expression for the universal \(R\)-matrix as a result of calculating the corresponding integrals.