Factorizing twists and the universal R-matrix of the Yangian Y(sl_2)

TL;DR

This paper constructs explicit factorizing twists for the Yangian Y(sl_2) in evaluation representations, providing a universal expression that recovers the universal R-matrix and is adaptable to broader contexts.

Contribution

It offers a universal, explicit construction of factorizing twists for Y(sl_2) applicable to all evaluation representations, including infinite-dimensional cases.

Findings

Universal expression for factorizing twists in Y(sl_2)

Method recovers the universal R-matrix in generic evaluation representations

Elementary operations enable easy generalizations

Abstract

We give an explicit construction of the factorizing twists for the Yangian Y(sl_2) in evaluation representations (not necessarily finite-dimensional). The result is a universal expression for the factorizing twist that holds in all these representations. The method is general enough to recover the universal R-matrix of Y(sl_2) up to its character in the form specialized to generic evaluation representations. The method presented here is particularly amenable to generalizations because it involves only elementary operations applied to representations of the Yangian.