%0 Journal Article
%T Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
%A Hiroshi Miki
%A Hiroaki Goda
%A Satoshi Tsujimoto
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X 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 2กม2 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.
%K skew orthogonal polynomials
%K discrete integrable systems
%K discrete coupled KP equation
%K Pfaff lattice
%K Christoffel-Darboux kernel
%U http://dx.doi.org/10.3842/SIGMA.2012.008