Imprimitively generated Lie-algebraic Hamiltonians and separation of variables
solv-int
2007-05-23 v1 Differential Geometry
Exactly Solvable and Integrable Systems
Abstract
Turbiner's conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example is given based on the trigonometric Olshanetsky-Perelomov potential corresponding to the A_2 root system.
Keywords
Cite
@article{arxiv.solv-int/9806003,
title = {Imprimitively generated Lie-algebraic Hamiltonians and separation of variables},
author = {Robert Milson},
journal= {arXiv preprint arXiv:solv-int/9806003},
year = {2007}
}
Comments
32 pages. To appear in the Canadian Journal of Mathematics