箱玉系と非自励離散戸田格子 (可積分系数理の深化と展開)

Abstract

We discuss the theory of finite orthogonal polynomials based on elementary linear algebra and its connection to the nonautonomous discrete Toda lattice with nonperiodic finite lattice boundary condition. By using the spectral transformation technique for finite orthogonal polynomials, one can give a solution to the initial value problem of the nonautonomous discrete Toda lattice. However, this construction of the solution cannot be ultradiscretized because of so-called “negative problem". In this paper, we focus on the rigged configuration technique to solve the initial value problem of the box-ball system and consider a connection between the rigged configuration and orthogonal polynomials.