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

Symmetry Integrability and Geometry-Methods and Applications

article

Hiroshi Miki¹  Hiroaki Goda¹  Satoshi Tsujimoto¹ 

[1] Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University

关键词: skew orthogonal polynomials;    discrete integrable systems;    discrete coupled KP equation;    Pfaf f lattice;    Christof fel–Darboux kernel;   

DOI  :  10.3842/SIGMA.2012.008

来源: National Academy of Science of Ukraine

【 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