Geometric construction of the classical r-matrix for the elliptic Calogero-Moser system
Arutyunov, Gleb
Banach Center Publications, Tome 38 (1997), p. 249-259 / Harvested from The Polish Digital Mathematics Library
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By applying the Hamiltonian reduction technique we derive a matrix first order differential equation that yields the classical r-matrices of the elliptic (Euler-) Calogero-Moser systems as well as their degenerations.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:252255 
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     author = {Arutyunov, Gleb},
     title = {Geometric construction of the classical r-matrix for the elliptic Calogero-Moser system},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {249-259},
     zbl = {0879.58030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p249bwm}
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Arutyunov, Gleb. Geometric construction of the classical r-matrix for the elliptic Calogero-Moser system. Banach Center Publications, Tome 38 (1997) pp. 249-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p249bwm/

[000] [1] E. K. Sklyanin, Alg. Anal., 6(2) (1994) 227.

[001] [2] H. W. Braden, T. Suzuki, Lett. Math. Phys. 30 (1994) 147.

[002] [3] E. Billey, J. Avan, O. Babelon, Phys. Lett. A 188 (1994) 263.

[003] [4] G. E. Arutyunov, P. B. Medvedev, Geometric construction of the classical r-matrix for the elliptic and trigonometric Calogero-Moser systems, preprint, hep-th/9511070.

[004] [5] V. I. Arnol'd, Mathematical methods of classical mechanics, Graduate Texts in Math., 60, Spinger-Verlag, Berlin, New-York, 1989.

[005] [6] M. A. Olshanetsky, A. M. Perelomov, Invent. Math. 37 (1976) 93; Phys. Reps. 71 (1981) 313; Phys. Reps. 94 (1983) 6; D. Kazhdan, B. Kostant, S. Sternberg, Comm. Pure Appl. Math. 31 (1978) 481.

[006] [7] J. Avan, O. Babelon, M. Talon, Alg. Anal., 6(2) (1994) 67.

[007] [8] E. Markman, Comp. Math. 93 (1994) 255.

[008] [9] A. Gorsky, N. Nekrasov, Elliptic Calogero-Moser system from two-dimensional current algebra, preprint, hep-th/9401021. | Zbl 1052.81607

[009] [10] O. Babelon, C. M. Viallet, Phys. Lett. B 237 (1989) 411.

[010] [11] J. Avan, M. Talon, Phys. Lett. B 303 (1993) 33.

[011] [12] I. Krichever, Funk. Anal. Appl., 14 (1980) 45.

[012] [13] N. I. Akhiezer, Elements of theory of elliptic functions, in Russian.

[013] [14] A. Gorsky, N. Nekrasov, Nucl. Phys. B414 (1994), 213; B436 (1995), 582; A. Gorsky, Integrable many body systems in the field theories, preprint UUITP-16/94, (1994). | Zbl 0855.35106

[014] [15] J. Avan and G. Rollet, The classical r-matrix for the relativistic Ruijsenaars-Schneider system, preprint BROWN-HET-1014 (1995). | Zbl 1073.81585

[015] [16] S. N. Ruijsenaars, Comm. Math. Phys. 110 (1987) 191.