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We calculate factorizing twists in evaluation representations of the quantumaffine algebra U_q(\hat sl_2). From the factorizing twists we derive arepresentation independent expression of the R-matrices of U_q(\hat sl_2).Comparing with the corresponding quantities for the Yangian Y(sl_2), it isshown that the U_q(\hat sl_2) results can be obtained by `replacing numbers byq-numbers'. Conversely, the limit q -> 1 exists in representations of U_q(\hatsl_2) and both the factorizing twists and the R-matrices of the Yangian Y(sl_2)are recovered in this limit.Comment: 19 pages, LaTe

Factorizing twists andR-matrices for representations of the quantum affine algebra $U_q(\widehat{\frak{sl}}_2)$