Abstract
We calculate explicit expressions for factorizing Drinfel’d twists in evaluation representations of the YangianY(sl2) and of the quantum affine algebraUq\(\left( {\widehat{\mathfrak{s}\mathfrak{l}}2} \right)\). From the twists we derive a closed and representation-independent form of theR-matrices in these representations. Employing a carefully chosen basis it is possible to recover the results for the Yangian (rational case) as theq → 1 limit of the expressions for the quantum affine algebra (trigonometric case).
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