  Let $G_M$ be one of the complex Lie groups $O_M$ and $Sp_M$. The irreducible
finite-dimensional representations of the group $G_M$ are labeled by partitions
$\mu$ satisfying certain extra conditions. Let $U$ be the representation of
$G_M$ corresponding to $\mu$. Regard the direct product $G_N\times G_M$ as a
subgroup of $G_{N+M}$. Let $V$ be the irreducible representation of $G_{N+M}$
corresponding to a partition $\lambda$. Consider the vector space
$W=Hom_{G_M}(U,V)$. It comes with a natural action of the group $G_N$. Let $n$
be sum of parts of $\lambda$ less the sum of parts of $\mu$. For any choice of
a standard Young tableau of skew shape $\lambda/\mu$, we realize $W$ as a
subspace in the tensor product of $n$ copies of the defining $N$-dimensional
representation of $G_N$. This subspace is determined as the image of a certain
linear operator $F(M)$ in the tensor product, given by an explicit formula.
When M=0 and $W=V$ is an irreducible representation of $G_N$, we recover the
classical realization of $V$ as a subspace in the space of all traceless
tensors. Then the operator F(0) can be regarded as the analogue for $G_N$ of
the Young symmetrizer, corresponding to the chosen standard tableau of shape
$\lambda$. Even in the special case M=0, our formula for the operator $F(M)$ is
new. Our results are applications of representation theory of the twisted
Yangian, corresponding to $G_N$. In particular, $F(M)$ is an intertwining
operator between two representations of the twisted Yangian in the $n$-fold
tensor product.
