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$% C. Dionisi, Stabilizers for nondegenerate matrices of boundary format and Steiner bundles, Rev. Mat. Complut. 17 (2004), 459469.%$

Stabilizers for Nondegenerate Matrices of Boundary Format and Steiner Bundles

Carla DIONISI
Dipartimento di Matematica Applicata “G. Sansone”
Via S. Marta, 3
I-50139, Firenze Italy

Received: February 25, 2002
Accepted: April 26, 2004
ABSTRACT

In this paper nondegenerate multidimensional matrices of boundary format in V0 ox  ... ox  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 ox  ... ox  Vp  such that       0
Stab(A)   (_  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 Ancona and Ottaviani (2001).

Key words: vector bundles, multidimensional matrices, theory of invariants.
2000 Mathematics Subject Classification:
14F05, 15A72.