Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables

Milson, Robert

Canadian journal of mathematics, Tome 50 (1998) no. 6, pp. 1298-1322

Résumé

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.

Détail

DOI : 10.4153/CJM-1998-063-2

Mots-clés : 35Q40, 53C30, 81R05

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