Irreducible characters and Clebsch-Gordan series for the exceptional algebra $E_6$: an approach through the quantum Calogero-Sutherland model

Details Irreducible characters and Clebsch-Gordan series for the exceptional algebra $E_6$: an approach through the quantum Calogero-Sutherland model Irreducible characters and Clebsch-Gordan series for the exceptional algebra $E_6$: an approach through the quantum Calogero-Sutherland model

2004-06-29

arxiv.org/abs/math-ph/0406067v1

Physics

Mathematical Physics

22 pages, 1 figure

Scientific paper

We re-express the quantum Calogero-Sutherland model for the Lie algebra $E_6$ and the particular value of the coupling constant $\kappa=1$ 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.

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