منابع مشابه
Hankel hyperdeterminants and Selberg integrals
Abstract. We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form Ai1i2...ik = f(i1+i2+· · ·+ik)). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg’s original formula amounts to the evaluation of all Ha...
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This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...
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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 2×2×2 hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this ...
متن کاملSummation formulas for Schur functions involving hyperdeterminants
We give general integral formulas involving for hyperdeterminants or hyperpfaffians. In the applications, we obtain several summation formulas for the products of Schur functions, which are generalizations of Cauchy’s determinant. Further, we study Toeplitz hyperdeterminants by using the theory of Jack polynomials and give a hyperdeterminant version of a strong Szegö limit theorem. MSC-class: p...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1996
ISSN: 0373-0956
DOI: 10.5802/aif.1526