  We study the tensor product $W$ of any number of "elementary" irreducible
modules $V_1,...,V_k$ over the Yangian of the general linear Lie algebra. Each
of these modules is determined by a skew Young diagram and a complex parameter.
For any indices $i,j=1,...,k$ there is a canonical non-zero intertwining
operator $A_{ij}$ between the tensor products $V_i\otimes V_j$ and $V_j\otimes
V_i$. This operator is defined up to a scalar multipler. We show that the
tensor product $W$ is irreducible, if and only if all operators $A_{ij}$ with
$i<j$ are invertible. This implies that the Yangian module $W$ is irreducible,
if and only if all pairwise tensor products $V_i\otimes V_j$ with $i<j$ are
irreducible. We also introduce the notion of a Durfee rank of a skew Young
diagram. For an ordinary Young diagram, this is the length of its main
diagonal.
