Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6

TL;DR

This paper explores the eigenfunctions of the quantum trigonometric Calogero-Sutherland model associated with the exceptional Lie algebra E6, using a parametrization based on fundamental characters.

Contribution

It extends the parametrization approach to the E6 Lie algebra, providing new insights into the model's eigenfunctions related to this exceptional algebra.

Findings

Eigenfunctions expressed in terms of fundamental characters.

New parametrization method for E6 related models.

Potential applications to mathematical physics and representation theory.

Abstract

The quantum trigonometric Calogero-Sutherland models related to Lie algebras admit a parametrization in which the dynamical variables are the characters of the fundamental representations of the algebra. We develop here this approach for the case of the exceptional Lie algebra E6.