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

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

2000-11-17

arxiv.org/abs/math-ph/0011029v1

J. Phys. A: Math. Gen. 34 (2001) 1753-1770

Physics

Mathematical Physics

19 pages, LaTeX

Scientific paper

10.1088/0305-4470/34/8/318

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.

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