On the R-matrix realization of the quantum loop algebra. The case of Uq(Dn(2))

The connection between the R-matrix realization and Drinfeld’s realization of the quantum loop algebra Uq(Dn(2)) is considered using the Gaussian decomposition approach proposed in Ding and Frenkel [Isomorphism of two realizations of quantum affine algebra Uq(gl̂(n)), Commun. Math. Phys. 156, 277 (1993)]. Our main result is a description of the embedding homomorphism which relates the quantum affine algebra of rank n − 1 with a subalgebra of the corresponding algebra of rank n. Explicit relations between all Gaussian coordinates of the L-operators and the currents are presented.