Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
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We calculate explicit expressions for factorizing Drinfel'd twists in evaluation representations of the Yangian YSymbol. 12 and of the quantum affine algebra UqSymbol. 12. From the twists we derive a closed and representation-independent form of the R-matrices in these representations. Employing a carefully chosen basis it is possible to recover the results for the Yangian (rational case) as the q→1 limit of the expressions for the quantum affine algebra (trigonometric case).