Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials
Mathematical Physics
2016-11-28 v2 High Energy Physics - Theory
math.MP
Representation Theory
Spectral Theory
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 and exceptional Lie algebras are FTI. This conjecture is also confirmed for the trigonometric Olshanetsky-Perelomov Hamiltonian whose algebraic form is found with the use of FTI.
Cite
@article{arxiv.0805.0770,
title = {Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials},
author = {K. G. Boreskov and A. V. Turbiner and J. C. Lopez Vieyra},
journal= {arXiv preprint arXiv:0805.0770},
year = {2016}
}
Comments
17 pages, to appear in Contemporary Mathematics