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

Symmetry, Integrability and Geometry: Methods and Applications

关键词: skew orthogonal polynomials;    discrete integrable systems;    discrete coupled KP equation;    Pfaff lattice;    Christoffel-Darboux kernel;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown