On the R-matrix realization of the quantum loop algebra. The case of $U_q(D^{(2)}_n)$

The connection between the R-matrix realization and Drinfeld's realization of the quantum loop algebra $U_q(D^{(2)}_n)$ is considered using the Gaussian decomposition approach proposed by J. Ding and I. B. Frenkel. Our main result is a description of the embedding $U_q(D^{(2)}_{n-1})\hookrightarrow U_q(D^{(2)}_n)$ that underlies this connection. Explicit relations between all Gaussian coordinates of the L-operators and the currents are presented.