On an approach for computing the generating functions of the characters of simple Lie algebras

TL;DR

This paper introduces a novel method based on the quantum trigonometric Calogero-Sutherland model to compute generating functions of characters for simple Lie algebras, demonstrated through low-rank classical examples.

Contribution

It presents a new approach leveraging integrable models to efficiently derive generating functions for Lie algebra characters.

Findings

Method successfully applied to low-rank classical algebras

Provides explicit generating functions for specific cases

Demonstrates practicality of the approach

Abstract

We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by means of a few examples involving some low rank classical algebras.