Quantum trigonometric Calogero-Sutherland model and irreducible characters for the exceptional algebra E8

TL;DR

This paper reformulates the quantum trigonometric Calogero-Sutherland model for E8 using fundamental characters as variables, and computes various characters of the algebra, advancing understanding of its representation theory.

Contribution

It expresses the E8 Hamiltonian in terms of fundamental irreducible characters and computes higher order characters, providing new tools for analyzing the algebra's structure.

Findings

Hamiltonian expressed via fundamental characters

Computed second order and higher order characters

Enhanced understanding of E8's representation theory

Abstract

We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E8 and coupling constant k=1 by using the fundamental irreducible characters of the algebra as dynamical independent variables. Then, we compute the second order characters of the algebra and some higher order characters.