  Olshanski's centralizer construction provides a realization of the Yangian
for the Lie algebra gl(n) as a subalgebra in the projective limit of a chain of
centralizers in the universal enveloping algebras. We give a modified version
of this construction based on a quantum analog of Sylvester's theorem. We then
use it to get an algebra homomorphism from the Yangian to the transvector
algebra associated with the general linear Lie algebras. The results are
applied to identify the elementary representations of the Yangian by
constructing their highest vectors explicitly in terms of elements of the
transvector algebra.
