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(D⁽²⁾ₙ) is considered using the Gaussian decomposition approach proposed by J. Ding and I. B. Frenkel. Our main result is a description of the embedding Uq(D⁽²⁾ₙ₋₁) Uq(D⁽²⁾ₙ) that underlies this connection. Explicit relations between all Gaussian coordinates of the L-operators and the currents are presented.