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

Abstract

We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}({\mathfrak{so}}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine algebra $U=U_{r,s}(\widehat{{\mathfrak{so}}_{2n}})$. Using the Gauss decomposition of the $R$-matrix realization of $U=U_{r,s}({\mathfrak{so}}_{2n})$, we study the commutation relations of the Gaussian generators and finally arrive at its $RLL$-formalism of the Drinfeld realization of two-parameter quantum affine algebra $U=U_{r,s}(\widehat{{\mathfrak{so}}_{2n}})$.

32 pages