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We give an explicit construction of the factorizing twists for the YangianY(sl_2) in evaluation representations (not necessarily finite-dimensional). Theresult is a universal expression for the factorizing twist that holds in allthese representations. The method is general enough to recover the universalR-matrix of Y(sl_2) up to its character in the form specialized to genericevaluation representations. The method presented here is particularly amenableto generalizations because it involves only elementary operations applied torepresentations of the Yangian.Comment: 25 pages, LaTe

Factorizing twists and the universalR-matrix of the YangianY(𝔰𝔩2)

Factorizing twists and the universalR-matrix of the YangianY(𝔰𝔩₂)