Hyperdeterminants as integrable discrete systems

Abstract

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2x2x2x2-hyperdeterminant.

Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstract

References in corpus (5)

• Hyperdeterminantal relations among symmetric principal minors
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• On reductions of the discrete Kadomtsev--Petviashvili-type equations
• Dispersionless (3+1)-dimensional integrable hierarchies
• Duality for discrete integrable systems II
• Discrete Darboux system with self-consistent sources and its symmetric reduction