dorsal/arxiv
View SchemaImprimitively generated Lie-algebraic Hamiltonians and separation of variables
| Authors | Robert Milson |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9806003 |
| URL | https://arxiv.org/abs/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.
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"abstract": "Turbiner\u0027s conjecture posits that a Lie-algebraic Hamiltonian operator whose\ndomain is a subset of the Euclidean plane admits a separation of variables. A\nproof of this conjecture is given in those cases where the generating\nLie-algebra acts imprimitively. The general form of the conjecture is false. A\ncounter-example is given based on the trigonometric Olshanetsky-Perelomov\npotential corresponding to the A_2 root system.",
"arxiv_id": "solv-int/9806003",
"authors": [
"Robert Milson"
],
"categories": [
"solv-int",
"math.DG",
"nlin.SI"
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"title": "Imprimitively generated Lie-algebraic Hamiltonians and separation of variables",
"url": "https://arxiv.org/abs/solv-int/9806003"
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