Stabilizers for nondegenerate matrices of boundary format and Steiner bundles

In this paper nondegenerate multidimensional matrices of boundary format in $V_0\otimes \mathrm{.}\mathrm{.}\mathrm{.}\otimes V_p$ are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix $A$ the stabilizer for the $SL(V_0)\times \mathrm{.}\mathrm{.}\mathrm{.}\times SL(V_p)$-action, $Stab(A)$, is completely described. In particular we prove that there exists an explicit action of SL(2) on $V_0\otimes \mathrm{.}\mathrm{.}\mathrm{.}\otimes V_p$ such that $Stab(A{)}^0\subseteq SL(2)$ and the equality holds if and only if $A$ belongs to a unique $SL(V_0)\times >\mathrm{.}\mathrm{.}\mathrm{.}\times SL(V_p)$-orbit containing the identity matrices.