Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7

TL;DR

This paper reformulates the quantum Calogero-Sutherland model for the exceptional Lie algebra E7 using irreducible characters as variables, providing a systematic method to compute characters and Clebsch-Gordan series.

Contribution

It introduces a systematic procedure to express the E7 model in terms of irreducible characters and to compute related Clebsch-Gordan series, advancing understanding of this exceptional algebra.

Findings

Re-expressed the E7 Calogero-Sutherland model using characters

Developed a method to compute Clebsch-Gordan series for E7

Enabled calculation of additional characters and series

Abstract

We re-express the quantum Calogero-Sutherland model for the Lie algebra E7 and the particular value of the coupling constant K=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra.