Stabilizers for Nondegenerate Matrices of Boundary Format and Steiner Bundles

Résumé

In this paper nondegenerate multidimensional matrices of boundary format in V0• • •Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) × • • • × SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 • • •Vp such that Stab(A)0 _ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) × • • • × SL(Vp)-orbit containing the identity matrices, according to [1].