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Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems

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Author(s): Hiroshi Miki | Hiroaki Goda | Satoshi Tsujimoto

Journal: Symmetry, Integrability and Geometry : Methods and Applications
ISSN 1815-0659

Volume: 8;
Start page: 008;
Date: 2012;
Original page

Keywords: skew orthogonal polynomials | discrete integrable systems | discrete coupled KP equation | Pfaff lattice | Christoffel-Darboux kernel

ABSTRACT
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2×2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations.

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