Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials

Abstract

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 $A_N,B_N,C_N,D_N,B{C}_N$ 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.

arXiv comment17 pages, to appear in Contemporary Mathematics

Cited by in corpus (1)

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