  We use the theory of skew duality to show that decomposing the tensor product
of $k$ irreducible representations of the symplectic group $Sp_{2m} =
Sp_{2m}(C)$ is equivalent to branching from $Sp_{2n}$ to
$Sp_{2n_1}\times\cdots\times Sp_{2n_k}$ where $n, n_1,\ldots, n_k$ are positive
integers such that $n = n_1+\cdots+n_k$ and the $n_j$'s depend on $m$ as well
as the representations in the tensor product. Using this result and a work of
J. Lepowsky, we obtain a skew Pieri rule for $Sp_{2m}$, i.e., a description of
the irreducible decomposition of the tensor product of an irreducible
representation of the symplectic group $Sp_{2m}$ with a fundamental
representation.
