Two-parameter Quantum Affine Algebra of Type ${\mathrm{C}}_n^{(1)},$ Drinfeld Realization and Vertex Representation

The two-parameter quantum vertex operator representation of level-one is explicitly constructed for $U_{r,s}(C_n^{(1)})$ based on its two-parameter Drinfeld realization we give. This construction will degenerate to the one-parameter case due to Jing-Koyama-Misra (\cite{JKM2}) when $rs=1$.