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

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