  In this paper, we first formulate a super version of Vust theorem associated
with a regular nilpotent element $e\in\mathfrak{gl}(V)$. As an application of
this theorem, we then obtain the Schur-Sergeev duality for principal finite
$W$-superalgebras which is partially a super version of Brundan-Kleshchev's
higher level Schur-Weyl duality.
