On differential operators for bivariate Chebyshev polynomials

TL;DR

This paper constructs specific differential operators for which bivariate Chebyshev polynomials related to Lie algebras $C_2$ and $G_2$ serve as eigenfunctions, advancing the understanding of their mathematical properties.

Contribution

It introduces differential operators for bivariate Chebyshev polynomials associated with Lie algebras $C_2$ and $G_2$, a novel connection in mathematical analysis.

Findings

Identified differential operators for Chebyshev polynomials of $C_2$ and $G_2$

Established eigenfunction relationships for these polynomials

Enhanced understanding of polynomial-Lie algebra connections

Abstract

We construct the differential operators for which bivariate Chebyshev polynomials of the first kind, associated with simple Lie algebras $C_2$ and $G_2$, are eigenfunctions.