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

J. Fernandez-Nunez·W. Garcia-Fuertes·A. M. Perelomov
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Abstract

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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BibTeXRIS

J. Fernandez-Nunez, W. Garcia-Fuertes, A. M. Perelomov. 2004-06-29. Irreducible characters and Clebsch-Gordan series for the exceptional algebra $E_6$: an approach through the quantum Calogero-Sutherland model. https://doi.org/10.2991/jnmp.2005.12.s1.23

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