$RLL$-realization of two-parameter quantum affine algebra in type $C_n^{(1)}$

TL;DR

This paper constructs an explicit link between two different algebraic presentations of the two-parameter quantum affine algebra of type C_n^{(1)}.

Contribution

It provides a detailed correspondence between the Drinfeld current algebra and the R-matrix realization for this algebra.

Findings

Established an explicit algebraic correspondence

Connected Drinfeld and R-matrix realizations

Clarified structure of two-parameter quantum affine algebra

Abstract

We establish an explicit correspondence between the Drinfeld current algebra presentation for the two-parameter quantum affine algebra $U_{r, s}(\mathrm{C}_n^{(1)})$ and the $R$-matrix realization \'a la Faddeev, Reshetikhin and Takhtajan.