Discrete spectral transformations of skew orthogonal polynomials and associated discrete integrable systems

Hiroshi Miki ; Hiroaki Goda ; Satoshi Tsujimoto

Symmetry, integrability and geometry: methods and applications, Tome 8 (2012)

Résumé

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 $2\times 2$ 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.

Détail

Keywords: skew orthogonal polynomials, discrete integrable systems, discrete coupled KP equation, Pfaff lattice, Christoffel–Darboux kernel.

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