Factorizing twists and R-matrices for representations of the quantum affine algebra Uq((sl)over-cap2)

We calculate factorizing twists in evaluation representations of the quantum affine algebra U-q((sl) over cap (2)). From the factorizing twists we derive a representation-independent expression of the R-matrices of U-q((sl) over cap (2)). Comparing with the corresponding quantities for the Yangian Y(sl(2)), it is shown that the U-q((sl) over cap (2)) results can be obtained by 'replacing numbers by q-numbers'. Conversely, the limit q --> 1 exists in representations of U-q((sl) over cap (2)) and both the factorizing twists and the R-matrices of the Yangian Y(sl(2)) are recovered in this limit.