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SUTHERLAND-TYPE TRIGONOMETRIC MODELS, TRIGONOMETRIC INVARIANTS AND MULTIVARIATE POLYNOMIALS III: E₈ CASE

Institute for Theoretical and Experimental Physics, Moscow 11259, Russia

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., Mexico

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J. C. LÓPEZ VIEYRA

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., Mexico

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, and

M. A. G. GARCÍA

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., Mexico

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https://doi.org/10.1142/S0217751X11053018Cited by:2 (Source: Crossref)

Abstract

It is shown that the E₈ trigonometric Olshanetsky–Perelomov Hamiltonian, when written in terms of the fundamental trigonometric invariants, is in algebraic form, i.e. it has polynomial coefficients, and preserves two infinite flags of polynomial spaces marked by the Weyl (co)-vector and E₈ highest root (both in the basis of simple roots) as characteristic vectors. The explicit form of the Hamiltonian in new variables has been obtained both by direct calculation and by means of the orbit function technique. It is shown the triangularity of the Hamiltonian in the bases of orbit functions and of algebraic monomials ordered through Weyl heights. Examples of first eigenfunctions are presented.

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