2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170618Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of the form R=(X^{-1} \otimes X^{-1}) Δ(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined in finite type. We give a similar formula which is valid for the quantized universal enveloping algebra of any symmetrizable Kac-Moody algebra. This is done by replacing the action of X on V with an endomorphism that preserves weight spaces, but which is bar-linear instead of linear.9 pages. v2: minor correctionsQuantum AlgebraRepresentation Theorytext