Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials

Details Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials

2008-05-06

arxiv.org/abs/0805.0770v2

Physics

Mathematical Physics

17 pages, to appear in Contemporary Mathematics

Scientific paper

It is conjectured that any trigonometric Olshanetsky-Perelomov Hamiltonian written in Fundamental Trigonometric Invariants (FTI) as coordinates takes an algebraic form and preserves an infinite flag of spaces of polynomials. It is shown that try-and-guess variables which led to the algebraic form of trigonometric Olshanetsky-Perelomov Hamiltonians related to root spaces of the classical $A_N, B_N, C_N, D_N, BC_N$ and exceptional $G_2, F_4$ Lie algebras are FTI. This conjecture is also confirmed for the trigonometric $E_6$ Olshanetsky-Perelomov Hamiltonian whose algebraic form is found with the use of FTI.

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