Commuting differential operators of rank 2 with polynomial coefficients

TL;DR

This paper explores self-adjoint commuting differential operators with polynomial coefficients, presenting new examples of rank 2 operators that expand understanding of their algebraic structure.

Contribution

The paper introduces novel examples of rank 2 commuting differential operators with polynomial coefficients, advancing the classification of such operators.

Findings

New examples of rank 2 commuting operators found

Operators define commutative subalgebras of the Weyl algebra

Enhances understanding of algebraic structures of differential operators

Abstract

In this paper we study self-adjoint commuting ordinary differential operators with polynomial coefficients. These operators define commutative subalgebras of the first Weyl algebra. We find new examples of commuting operators of rank 2.