Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7
arXiv:math-ph/0507015 · doi:10.1063/1.2036947
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