Singular R-matrices and Drinfeld's comultiplication

TL;DR

This paper computes a specific R-matrix for U_q(sl_2) and constructs an algebra A(R) that is isomorphic to an extension of Drinfeld's algebra, advancing understanding of quantum affine algebras.

Contribution

It explicitly calculates the R-matrix for evaluation representations and establishes an isomorphism between A(R) and an extended Drinfeld algebra.

Findings

Explicit R-matrix with delta-function terms

Construction of algebra A(R) with relations from R

Isomorphism between A(R) and extended Drinfeld algebra

Abstract

We compute the R-matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for U_q(\widehat{sl}_2). This R-matrix contains terms proportional to the delta-function. We construct the algebra A(R) generated by the elements of the matrices L^\pm(z) with relations determined by R. In the category of highest weight representations, there is a Hopf algebra isomorphism between A(R) and an extension \overline{U}_q(\widehat{sl}_2)} of Drinfeld's algebra.