Matrix Orthogonal Polynomial in the theory of Full Kostant-Toda Systems

TL;DR

This paper characterizes the full Kostant-Toda system using matrix orthogonal polynomials, providing explicit solutions and representations that deepen understanding of this dynamical system.

Contribution

It introduces a novel characterization of the Kostant-Toda system through matrix orthogonal polynomials and derives explicit solution formulas and functional representations.

Findings

Explicit Weyl function expressions for the system

Representation of the associated vector of linear functionals

Conditions for the existence of these representations

Abstract

In this work we characterize a full Kostant-Toda system in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system we give explicit expressions for the Weyl function and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system.