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

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.

37 pages, 1 figure

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Cited by in corpus (3)

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• On an approach for computing the generating functions of the characters of simple Lie algebras
• Sutherland Models for Complex Reflection Groups