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Liouville integrability of classical Calogero-Moser models. (English) Zbl 0972.81216

Summary: Liouville integrability of classical Calogero-Moser models is proved for models based on any root system, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e., untwisted and twisted together with their degenerations (hyperbolic, trigonometric and rational), except for the rational potential models confined by a harmonic force.

MSC:

81V70 Many-body theory; quantum Hall effect
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:

[1] Calogero, F.; Sutherland, B.; Moser, J.; Moser, J.; Calogero, F.; Marchioro, C.; Ragnisco, O.; Calogero, F., Integrable systems of non-linear evolution equations, (), Lett. nuovo cimento, Lett. nuovo cimento, 13, 411, (1975)
[2] Olshanetsky, M.A.; Perelomov, A.M.; Olshanetsky, M.A.; Perelomov, A.M., Invent. math., Phys. rep., 94, 313, (1983)
[3] van Diejen, J.F.; Vinet, L., Calogero – moser – sutherland models, (2000), Springer
[4] Khastgir, S.P.; Pocklington, A.J.; Sasaki, R., J. phys. A, 33, 9033, (2000)
[5] Bordner, A.J.; Corrigan, E.; Sasaki, R., Prog. theor. phys., 102, 499, (1999)
[6] Bordner, A.J.; Corrigan, E.; Sasaki, R.; Bordner, A.J.; Sasaki, R.; Takasaki, K.; Bordner, A.J.; Sasaki, R.; Khastgir, S.P.; Sasaki, R.; Takasaki, K., Prog. theor. phys., Prog. theor. phys., Prog. theor. phys., Prog. theor. phys., 102, 749, (1999)
[7] D’Hoker, E.; Phong, D.H., Nucl. phys. B, 530, 537, (1998)
[8] Olshanetsky, M.A.; Perelomov, A.M., Funct. anal. appl., 12, 121, (1977)
[9] Hurtubise, J.C.; Markman, E., 1999
[10] Ochiai, H.; Oshima, T.; Sekiguchi, H.; Oshima, T.; Sekiguchi, H., Proc. jpn. acad. ser. A math. sci., J. math. sci. univ. Tokyo, 2, 1, (1995)
[11] Inozemtsev, V.I., Lett. math. phys., 17, 11, (1989)
[12] Krichever, I.M., Funct. anal. appl., 14, 282, (1980)
[13] Flatto, L.; Wiener, M.M.; Flatto, L., Amer. J. math., Amer. J. math., 92, 552, (1970)
[14] Humphreys, J.E., Reflection groups and Coxeter groups, (1990), Cambridge University Press Cambridge · Zbl 0725.20028
[15] Shioda, T., J. math. soc. jpn., 43, 673, (1991)
[16] Berezin, F.A., Trudy moskov. mat. obshch., 6, 371, (1957)
[17] Avan, J.; Talon, M.; Avan, J.; Babelon, O.; Talon, M., Phys. lett. B, Algebra anal., 6, 67, (1994)
[18] Sklyanin, E.K.; Braden, H.W.; Suzuki, T., Algebra anal., Lett. math. phys., 30, 147, (1994)
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