1. CJM 1998 (vol 50 pp. 1298)
|Imprimitively generated Lie-algebraic Hamiltonians and separation of variables |
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.
Categories:35Q40, 53C30, 81R05