Factorizing twists and R-matrices for representations of the quantum affine algebra U_q(\hat sl_2)

TL;DR

This paper computes factorizing twists and R-matrices for evaluation representations of the quantum affine algebra U_q(sl_2), providing a q-deformation perspective and connecting to Yangian results.

Contribution

It derives a representation-independent expression for R-matrices of U_q(sl_2) from factorizing twists, linking quantum affine algebra and Yangian structures.

Findings

Explicit factorizing twists for U_q(sl_2) are calculated.

Representation-independent R-matrices are derived from these twists.

The q  1 limit recovers Yangian results.

Abstract

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.