Laurent skew orthogonal polynomials and related symplectic matrices

TL;DR

This paper introduces a special class of Laurent skew orthogonal polynomials with symmetry properties, explores their role as eigenfunctions of symplectic eigenvalue problems, and links them to butterfly matrices representing symplectic matrices.

Contribution

It presents a new class of Laurent skew orthogonal polynomials with symmetry and connects them to symplectic eigenvalue problems and butterfly matrices, advancing understanding of symplectic matrix structures.

Findings

Laurent skew orthogonal polynomials with Laurent symmetry are introduced.

These polynomials serve as eigenfunctions of symplectic generalized eigenvalue problems.

Modified polynomials relate to butterfly matrices, a canonical form of symplectic matrices.

Abstract

Particular class of skew orthogonal polynomials are introduced and investigated, which possess Laurent symmetry. They are also shown to appear as eigenfunctions of symplectic generalized eigenvalue problems. The modification of these polynomials gives some symplectic eigenvalue problem and the corresponding matrix is shown to be equivalent to butterfly matrix, which is a canonical form of symplectic matrices.