On calculation of generating functions of generalized Chebyshev polynomials in several variables

TL;DR

This paper introduces a novel method for calculating generating functions of generalized Chebyshev polynomials in multiple variables linked to root systems of simple Lie algebras, with explicit results for C_2 and G_2.

Contribution

A new computational approach for generating functions of multivariable Chebyshev polynomials related to Lie algebra root systems, including explicit cases for C_2 and G_2.

Findings

Derived generating functions for C_2 and G_2

Proposed a general method applicable to multiple variables

Enhanced understanding of polynomial structures in Lie algebra contexts

Abstract

We propose a new method of calculation of generating functions of Chebyshev polynomials in several variables associated with root systems of simple Lie algebras. We obtain the generating functions of the polynomials in two variables corresponding to the Lie algebras C_2 and G_2.