$RLL$-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 $U=U_{r,s}(\widehat{{\mathfrak{so}}_{2n}})$.

arXiv comment32 pages

References in corpus (5)

• Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
• Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: type C
• Notes on two-parameter quantum groups, (II)
• Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$

Cited by in corpus (1)

• $RLL$-Realization and Its Hopf Superalgebra Structure of $U_{p,q}(\widehat{\mathfrak{gl}(m|n))}$