$RLL$-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 $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. Using the Gauss decomposition of the $R$-matrix realization of $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$, 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 $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$.