  In this paper are introduced two classes of elements in the enveloping
algebra $\mathbf{U}(gl(n))$: the \emph{double Young-Capelli bitableaux} $[\
\fbox{$S \ | \ T$}\ ]$ and the \emph{central} \emph{Schur elements}
$\mathbf{S}_{\lambda}(n)$, that act in a remarkable way on the highest weight
vectors of irreducible Schur modules.
  Any element $\mathbf{S}_{\lambda}(n)$ is the sum of all double Young-Capelli
bitableaux $[\ \fbox{$S \ | \ S$}\ ]$, $S$ row (strictly) increasing Young
tableaux of shape $\widetilde{\lambda}$. The Schur elements
$\mathbf{S}_\lambda(n)$ are proved to be the preimages - with respect to the
Harish-Chandra isomorphism - of the \emph{shifted Schur polynomials}
$s_{\lambda|n}^* \in \Lambda^*(n)$. Hence, the Schur elements are the same as
the Okounkov \textit{quantum immanants}, recently described by the present
authors as linear combinations of \emph{Capelli immanants}. This new
presentation of Schur elements/quantum immanants doesn't involve the
irreducible characters of symmetric groups. The Capelli elements
$\mathbf{H}_k(n)$ are column Schur elements and the Nazarov-Umeda elements
$\mathbf{I}_k(n)$ are row Schur elements. The duality in
$\boldsymbol{\zeta}(n)$ follows from a combinatorial description of the
eigenvalues of the $\mathbf{H}_k(n)$ on irreducible modules that is {\it{dual}}
(in the sense of shapes/partitions) to the combinatorial description of the
eigenvalues of the $\mathbf{I}_k(n)$.
  The passage $n \rightarrow \infty$ for the algebras $\boldsymbol{\zeta}(n)$
is obtained both as direct and inverse limit in the category of filtered
algebras, via the \emph{Olshanski decomposition/projection}.
