  Two super-analogs of the Schur-Weyl duality are considered: the duality of
actions in $(\mathbb{C}^{m|n})^{\otimes N}$ of the Lie superalgebra
$\mathfrak{gl}(m,n)$ and the symmetric group $S_N$, and the duality of actions
of the Lie superalgebra $Q(n)$ and a certain finite group $Se(N)$ in
$(\mathbb{C}^{n|n})^{\otimes N}$. We construct an isomorphism of symmetric and
universal enveloping algebras of these Lie superalgebras called special
symmetrization. Using this isomorphism of vector spaces we describe explicitly
the duality between the centers of the corresponding universal enveloping
algebras and the group algebras.
