Factorizing twists and R-matrices for representations of the quantum affine algebra U_q(hat sl₂)

We calculate factorizing twists in evaluation representations of the quantum affine algebra U_q(\hat sl_2). From the factorizing twists we derive a representation independent expression of the R-matrices of U_q(\hat sl_2). Comparing with the corresponding quantities for the Yangian Y(sl_2), it is shown that the U_q(\hat sl_2) results can be obtained by `replacing numbers by q-numbers'. Conversely, the limit q -> 1 exists in representations of U_q(\hat sl_2) and both the factorizing twists and the R-matrices of the Yangian Y(sl_2) are recovered in this limit.