Christoffel transformations for (partial-)skew-orthogonal polynomials and applications

TL;DR

This paper explores Christoffel transformations applied to skew-orthogonal and partial-skew-orthogonal polynomials, revealing their role as spectral problems for discrete integrable hierarchies and deriving related integrable systems.

Contribution

It introduces the use of Christoffel transformations as spectral problems for skew-orthogonal polynomials and derives associated integrable hierarchies, expanding the theoretical framework.

Findings

Christoffel transformations act as spectral problems for discrete integrable hierarchies

Derivation of integrable hierarchies from skew-orthogonal polynomial transformations

Analysis of reductional cases within the framework

Abstract

In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transformations can act as spectral problems for discrete integrable hierarchies, and therefore we derive certain integrable hierarchies from these transformations. Some reductional cases are also considered.