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

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 2x2 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.

References in corpus (3)

• Auxiliary Linear Problem, Difference Fay Identities and Dispersionless Limit of Pfaff-Toda Hierarchy
• Linear problems and Bäcklund transformations for the Hirota-Ohta system
• Generalized Christoffel-Darboux formula for classical skew-orthogonal polynomials

Cited by in corpus (3)

• Direct Connection between the R_{II} Chain and the Nonautonomous Discrete Modified KdV Lattice
• Nonautonomous ultradiscrete hungry Toda lattice and a generalized box-ball system
• Christoffel transformations for (partial-)skew-orthogonal polynomials and applications