  We construct and study the holomorphic discrete series representation and the
principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$
over a $p$-adic field $F$ as well as a duality between some sub-representations
of these two representations. The constructions of these two representations
generalize those defined in Morita and Murase's works. Moreover, Morita built a
duality for $\mathrm{SL}(2, F)$ defined by residues. We view the duality we
defined as an algebraic interpretation of Morita's duality in some extent and
its generalization to the symplectic groups.
