Imprimitively generated Lie-algebraic Hamiltonians and separation of variables
arXiv:solv-int/9806003
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.
32 pages. To appear in the Canadian Journal of Mathematics